The tradition comes from a curious text called the Acts of (Judas) Thomas, which was written before 226 CE — at worst, approximately two hundred years after the events it purports to tell, even if it may be earlier. We have no (as far as I know) mention of this Indian mission in traditions that can be securely placed 200. As you may notice, this is a long time, especially for oral tradition, which has a tendency to dissolve truth it contains very fastly. However, if we want to salvage (or at least to try to) something from the text, we can notice that the narrative kernel in the Acts boils down to the following elements: Thomas sailed to India in the boat of a merchant called Habbam (whence? we don't know, but Mesopotamia and Yemen have been proposed), where he met a king called Gudnaphar (also known as Gondophares) and his brother Gad.

As I have said, if you are trying to assess the reliability of the text on the basis of purely internal evidence, you are probably going to conclude that it is bogus, and think that the Indian elements were made up later. However, we happen to know that a king called Gudnaphar ruled from 20 CE to after 46 (thanks to epigraphic evidence—however, this dating is contested), an ideal timeframe for Thomas' trip. We also have coin issues that mention Gudnaphar with the title Gadana. On the one hand, I must admit that this is quite compelling evidence—given the usual imprecision of writings on distant cultures in Antiquity, managing to achieve this degree of historical precision strongly suggests the existence of contemporary independent written source. On the other, the mishandling of information suggests that this source could have had nothing to do with pastoral concerns (it could have been a travelogue, for instance), and that the writter of the Acts did his homework well to create verisimilitude. An intermediate position would be to assume (quite reasonably, in fact) that Thomas, or a 1st-century Christian who knew the area, only had a dim vision of who was king, and therefore committed the initial misinterpretation of Gadana as a personal name.

As for your question on Thomas' itinerary, the capital of Gondophares' kingdom (Taxila) was situated in modern Pakistan. Even if we are sanguine about the value of the Acts, nothing it says on Thomas' adventures that can point to more eastern ventures (except for the existence of christians in South India who apparently say that their communities were created by Thomas; but I strongly suspect that this may be a contamination by Westerners).