I have researched St Thomas for family reasons (my mother went to a Catholic School in Australia called St Thomas's), and have personally visited the site of his believed martyrdom in Chennai in India.
There is a good account of the various explanations of Thomas's activities after the death of Jesus, contained in the Catholic Online Encyclopedia at:St Thomas
Nowhere there or elsewhere have I found it mentioned that he preached in India or China. It would appear the first Christians to reach China were in fact Nestorians, some time after the 4th century AD.
St Thomas is definitely associated with India, and it is believed he preached in India as far south as Madras (now Chennai). On the outskirts of Chennai is a hill called St Thomas Mount, and it was on this site that he was martyred by being pierced with spears. Alternative versions say he was martyred with arrows. When the Portuguese excavated the site in the 16th century they found this bas-relief cross which is inscribed in Old Sassanid Pahlavi.
Stylistically, the cross is very interesting. The columns on either side of the cross are very similar to the architecture of places like Palmyra, which is not that far from Edessa, where his remains were claimed to have been finally interred. The pillars are topped with flames, and there is a dove above the cross. The cross is strangely shaped, as it has balls on each end of what would otherwise look like a flory cross.
Some suggestions date the cross to the 7th century, but legend claims that it was before this cross that St Thomas was martyred. In any event, the cross certainly pre-dated the Portuguese arrival, although whether it dates to the 1st century AD is unknown. It could be possible, based on the language, but I cannot prove it.