Possible extrapolation of old German word "hansa" to protogermanic and possibly common root with Sanskrit "sangha"

Question

I came across a discussion about if "Lufthansa" means air-Swan, inspired by the sanskrit word hansa swan. Which is of course wrong as it has its origins in the old german word hansa for group or fellowship. But inspired by the question I thought about which would be the sanskrit "version" of the word (in the sense of which one might have come from the same origin, I miss the term sry). My idea was sangha, it means also group and the like and it would also match the s/k,h phonetic change as suggested by satem-kentum. My questions are

1. How far can we extrapolate the old german word hansa back to pre-germanic languages how would it have sounded there?
2. Could it be that hansa and sangha have a common origin?
3. Where comes Sanskrit sangha from?

(I am no expert for linguistics, so please apologize eventually wrong terms or conceptions, I am happy to learn about how to do it better)

Answer 1

Sangha is from Sanskrit *saṃ- (PIE *sem) "together" + *han- (PIE *gʷʰén) "strike, kill", and originally in Sanskrit meant "struck, put together". Hansa (referring to the Hanseatic league) is reconstructed to Proto-Germanic *hansō, and deeper relations are speculative. Germanic *h would derive from either PIE *k or *k'; PIE *k becomes Skt. [k] and PIE *k' appears as [ś] in Skt (*š in the Iranian branch). If a Sanskrit word with [ś] were actually related to a Germanic word with *h (*x), we would have to conclude that at least one of the words was a borrowing from another language. For example, path is clearly derived from IE *pent, but the consonant phonology is wrong for native Germanic development, and it is hypothesized that the Germanic word comes through Iranian. Despite the meaning similarities, the historical sound differences indicate that the words are unrelated.