From what I understand there really isn't enough clear cut information to figure out who they really were. There have been speculations based on some evidence/reasoning which have been contentious.
Some have drawn connection between pyrrhonism of pyrrho and early Buddhism (or potentially what would be "true" early Buddhism). The idea is that it might be Buddhists whom pyrrho met. There are lot of ink spilled on this topic.
Here's some back and forth on this idea: https://www.reddit.com/r/askphilosophy/comments/sby36p/what_are_the_western_parallels_of_buddhistic/hu3p2w1/ (See the context too)
There are academic books such as these going forth with this idea:
https://www.amazon.com/dp/B009W3SAKS/ref=dp-kindle-redirect?_encoding=UTF8&btkr=1
Another option that I referred to in the comment, is that they could be related to Ajnana schools (who were basically some of the earliest sceptics we have records of, Buddhists had some skeptical tendencies but not fully skeptics: David Kalupahana noted that Buddhism allowed a more pragmatic form of skepticism and it was a movement that was attractive to more skeptically-minded people. In fact some of Buddha's main disciples were supposedly initially from the skeptical school).
But there isn't much surviving record of Ajnana outside polemical context.
Here's one note (linked in the comment above) discussing potential link between Sanjaya's school and Pyrrho: http://www.unipune.ac.in/snc/cssh/ipq/english/IPQ/26-30%20volumes/30-3/30-3-7.pdf
(Note that I haven't dug too deep into the for side of pryrrho-Buddhism connection so IDK how much good evidence/research they have. I will leave it to you to check these out and decide for yourself).
Well, that's a very sensible question but, of course, another that could potentially take a PhD thesis to answer properly. But I'll have a go at giving a quick comment. Basically, we just don't know for sure. There were certainly more links than people typically assume between ancient eastern and western thought. The problem is that Parthia was in the way, actively blocking contact between the far east and the Roman empire.
When Alexander conquered Persia he took several philosophers with them, including Pyrrho, the founder of Skepticism. So there's a lot of interest in (and several books about) the idea that Pyrrho may have been influenced by eastern thought, which could have been quite different from what we think of as Hinduism or Buddhism today.
It's harder to trace a direct connection with Stoicism but Stoicism was influenced by Greek Skepticism so there would be an indirect connection. Stoicism was actually perceived by Athenians as a near eastern (Phoenician) philosophy, incidentally, and as somewhat "foreign" at Athens. It's likely influenced by Phoenician culture, but we don't know exactly how. You might want to check out things like the claim Apollonius of Tyana, during the Roman empire, travelled to India to study under the gymnosophoi (naked wise men). Or one report that Socrates debated with an Indian merchant. Also, evidence that Greek settlers engaged with Buddhist wise men, such as the Questions of King Milinda. There are many obscure links. Not long after Marcus Aurelius, we have Manichaeism, an influential hybrid of Christianity, Zoroastrianism, and Buddhism.
In other trivia, Marcus Aurelius had a Greek secretary called Alexander Peloplaton, a Sophist, whom we're told travelled widely, including to Egypt and Ethiopia, and met gymnosophoi, although it's not clear if that means travelling Indian wise men or just naked sages from Africa.