I invite you to guess or recall the answers, without looking them up, and post in comments.
India
http://en.wikipedia.org/wiki/Christianity_in_India#The_Arrival_of_St._Thomas
"According to Indian Christian traditions, the apostle Thomas arrived in Kodungallur (also Muziris), Kerala, established the Seven Churches and evangelized in present day Kerala and Tamil Nadu.[14]
As with early Christianity in the Roman Empire, it is assumed that the initial converts were largely Jewish proselytes among the Cochin Jews who are believed to have arrived in India around 562 BC, after the destruction of the First Temple.[15][16] Many of these Jews presumably spoke Aramaic like St. Thomas, also a Jew by birth, who is credited by tradition with evangelizing India.
A historically more likely claim by Eusebius of Caesarea is that Pantaenus, the head of the Christian exegetical school in Alexandria, Egypt went to India during the reign of the Emperor Commodus and found Christians already living in India using a version of the Gospel of Matthew with "Hebrew letters."[17] This is a plausible reference to the earliest Indian churches which are known to have used the Syriac New Testament. Pantaenus' evidence thus indicates that Syriac-speaking Christians had already evangelized parts of India by the late 2nd century."
"The South Indian epic of Manimekalai (written between 2nd and 3rd century AD) mentions the Nasrani people by referring to them by the name Essanis. "
http://en.wikipedia.org/wiki/Acts_of_Thomas
"Bar-Daisan (154–223) reports that in his time there were Christian tribes in North India which claimed to have been converted by Thomas and to have books and relics to prove it.[2] But at least by the year of the establishment of the Second Persian Empire (226), there were bishops of the Church of the East in northwest India, Afghanistan and Baluchistan, with laymen and clergy alike engaging in missionary activity"
http://en.wikipedia.org/wiki/Knanaya
"Thekkumbagar/Knanaya or more accurately Q'nanaya, (Heb:חנניה, Malayalam: ക്നാനായ, Syriac:ܛܢܢܐ, Ar:قينان) from Kerala, India, are a Jewish Christian people which claims early endogamous Kenite descent.[4][5] Their heritage and culture is Jewish-Keralite and their language Malayalam and Aramaic.[5] Their loyalties are with the Nasrani community of Syriac Christians from Kerala.[5]"
"Nasrani had already arrived on the Malabar coast before the traditional 345CE migration date of the Knanaya and included native Indian converts and converted Jewish people - Sephardi, Paradesi, and Cochin Jews - who had settled in Kerala during the Babylonian exile and increasing persecution in Europe.[6] They came mostly from the Northern Kingdom of Israel and became known as Northists."
So, quite possibly first century, pretty definitely by the third.
China
http://en.wikipedia.org/wiki/Christianity_in_China#Pre-modern_history
"The first documented case of Christianity entering China was in the 7th century, which is known from the Nestorian Stele, a stone tablet created in the 8th century. It records that Christians reached the Tang dynasty capital Xian in 635 and were allowed to establish places of worship and to propagate their faith. The leader of the Christian travelers was Alopen.[4]"
http://en.wikipedia.org/wiki/Alopen
"Nestorianism disappeared with the fall of the Tang Dynasty in the early 10th century. It did not return for three centuries, when it was reintroduced by the Mongols"
7th century.
Japan
http://search.japantimes.co.jp/cgi-bin/fv20010724a2.html
"Yet, Joseph says it was the uncovering of the Da Qin monastery in Xian, China that has provided the most conclusive evidence that the church made it here. The two Chinese characters for Da Qin, he says, correspond to "Uzumasa" in Japanese. Uzumasa-dera is one of the names given to a Kyoto temple long thought to have once been a place of Christian worship. Even today there are remnants there indicating its Christian past, Joseph says.
Built at the beginning of the 7th century, the temple, better known today as Koryu-ji, was founded by Hata no Kawakatsu, a member of the influential Hata family, whose more important members are thought to have arrived in Japan from Korea in AD 400.
However, in a book penned in the 1960s, Kyoto professor Ikeda claims that the Hata clan were from Turkestan. "The Hatas were a Nestorian tribe who . . . migrated to Japan via China and Korea in search of religious freedom," Ikeda writes. "Although they were persecuted by Buddhists in both China and Korea, they were granted full freedom in all but name from the time of their arrival."
The temple also housed a shrine to St. David and a holy well upon which stood a sacred tripod symbolizing the holy Trinity, Ikeda says. A tripod, built in the style of a triangular "torii," can still be seen at the temple today.
While both concentrate largely on interpreting relics and documents found in China, Saeki, who studied both the Persian and Syriac languages at Oxford University to help his studies in Eastern Christianity, also notes Imperial records in Japan that mark the visit of a Persian missionary to Nara in AD 736."
I put less faith in that article than I do in (sourced) Wikipedia summaries, honestly. I note that 400 would be well before Alopen's mission to the Tang. OTOH, with 2nd century Rome-China-India trade through the Kushans, and general maritime contact between India and China, Christianity reaching Japan before 1500s Europeans isn't impossible. I'm agnostic on this one.
India
http://en.wikipedia.org/wiki/Christianity_in_India#The_Arrival_of_St._Thomas
"According to Indian Christian traditions, the apostle Thomas arrived in Kodungallur (also Muziris), Kerala, established the Seven Churches and evangelized in present day Kerala and Tamil Nadu.[14]
As with early Christianity in the Roman Empire, it is assumed that the initial converts were largely Jewish proselytes among the Cochin Jews who are believed to have arrived in India around 562 BC, after the destruction of the First Temple.[15][16] Many of these Jews presumably spoke Aramaic like St. Thomas, also a Jew by birth, who is credited by tradition with evangelizing India.
A historically more likely claim by Eusebius of Caesarea is that Pantaenus, the head of the Christian exegetical school in Alexandria, Egypt went to India during the reign of the Emperor Commodus and found Christians already living in India using a version of the Gospel of Matthew with "Hebrew letters."[17] This is a plausible reference to the earliest Indian churches which are known to have used the Syriac New Testament. Pantaenus' evidence thus indicates that Syriac-speaking Christians had already evangelized parts of India by the late 2nd century."
"The South Indian epic of Manimekalai (written between 2nd and 3rd century AD) mentions the Nasrani people by referring to them by the name Essanis. "
http://en.wikipedia.org/wiki/Acts_of_Thomas
"Bar-Daisan (154–223) reports that in his time there were Christian tribes in North India which claimed to have been converted by Thomas and to have books and relics to prove it.[2] But at least by the year of the establishment of the Second Persian Empire (226), there were bishops of the Church of the East in northwest India, Afghanistan and Baluchistan, with laymen and clergy alike engaging in missionary activity"
http://en.wikipedia.org/wiki/Knanaya
"Thekkumbagar/Knanaya or more accurately Q'nanaya, (Heb:חנניה, Malayalam: ക്നാനായ, Syriac:ܛܢܢܐ, Ar:قينان) from Kerala, India, are a Jewish Christian people which claims early endogamous Kenite descent.[4][5] Their heritage and culture is Jewish-Keralite and their language Malayalam and Aramaic.[5] Their loyalties are with the Nasrani community of Syriac Christians from Kerala.[5]"
"Nasrani had already arrived on the Malabar coast before the traditional 345CE migration date of the Knanaya and included native Indian converts and converted Jewish people - Sephardi, Paradesi, and Cochin Jews - who had settled in Kerala during the Babylonian exile and increasing persecution in Europe.[6] They came mostly from the Northern Kingdom of Israel and became known as Northists."
So, quite possibly first century, pretty definitely by the third.
China
http://en.wikipedia.org/wiki/Christianity_in_China#Pre-modern_history
"The first documented case of Christianity entering China was in the 7th century, which is known from the Nestorian Stele, a stone tablet created in the 8th century. It records that Christians reached the Tang dynasty capital Xian in 635 and were allowed to establish places of worship and to propagate their faith. The leader of the Christian travelers was Alopen.[4]"
http://en.wikipedia.org/wiki/Alopen
"Nestorianism disappeared with the fall of the Tang Dynasty in the early 10th century. It did not return for three centuries, when it was reintroduced by the Mongols"
7th century.
Japan
http://search.japantimes.co.jp/cgi-bin/fv20010724a2.html
"Yet, Joseph says it was the uncovering of the Da Qin monastery in Xian, China that has provided the most conclusive evidence that the church made it here. The two Chinese characters for Da Qin, he says, correspond to "Uzumasa" in Japanese. Uzumasa-dera is one of the names given to a Kyoto temple long thought to have once been a place of Christian worship. Even today there are remnants there indicating its Christian past, Joseph says.
Built at the beginning of the 7th century, the temple, better known today as Koryu-ji, was founded by Hata no Kawakatsu, a member of the influential Hata family, whose more important members are thought to have arrived in Japan from Korea in AD 400.
However, in a book penned in the 1960s, Kyoto professor Ikeda claims that the Hata clan were from Turkestan. "The Hatas were a Nestorian tribe who . . . migrated to Japan via China and Korea in search of religious freedom," Ikeda writes. "Although they were persecuted by Buddhists in both China and Korea, they were granted full freedom in all but name from the time of their arrival."
The temple also housed a shrine to St. David and a holy well upon which stood a sacred tripod symbolizing the holy Trinity, Ikeda says. A tripod, built in the style of a triangular "torii," can still be seen at the temple today.
While both concentrate largely on interpreting relics and documents found in China, Saeki, who studied both the Persian and Syriac languages at Oxford University to help his studies in Eastern Christianity, also notes Imperial records in Japan that mark the visit of a Persian missionary to Nara in AD 736."
I put less faith in that article than I do in (sourced) Wikipedia summaries, honestly. I note that 400 would be well before Alopen's mission to the Tang. OTOH, with 2nd century Rome-China-India trade through the Kushans, and general maritime contact between India and China, Christianity reaching Japan before 1500s Europeans isn't impossible. I'm agnostic on this one.