History: During Alexander’s invasions, would his soldiers have found Old Persian or Indic to be somewhat familiar sounding given their closeness to Greek?

Good insight, Sabeshan. Probably.  And they probably wouldn’t have cared.

300 BC was a good time to be doing historical linguistics. The Indo-European languages were a lot closer to each other back then than they are now. In fact, the only reason Indo-European was discovered and reconstructed when it was, was that we had 2000 and 3000 year old records of Indo-European languages.

And the Greeks were well placed to do historical linguistics. They were already familiar with lots of different dialects of Greek, and the regular phonological correspondences between them.

But the Greeks did not make much of  historical linguistics.

• For starters, they didn’t really have the wherewithal for linguistic analysis. Linguistics as we know it is a Roman-era invention. The sophists got language analysis started in Classical time, but it was quite rudimentary. Aristophanes in his Frogs makes fun of Euripides’ new-fangled, sophist-inspired notions. Those notions include word and verse.
• For seconds, they were profoundly indifferent to the barbarians’ languages. They were, after all, bar-bar-bar gibberish. Herodotus records some Persian and Scythian derivations of names, so Greeks did learn languages; but they didn’t at the time particularly reflect on them. I think some Greek somewhere did speculate on Latin being a Greek dialect, because of the similarities; but that was later.
• For thirds, reflecting on the relatedness of languages is a very recent thing. The identification of Indo-European and Uralic languages as families is a very late thing—18th century.
• For fourths, if all the languages you’ve been exposed to are Indo-European, then your conclusion is that all languages  in the world have vaguely similar words for “mother” and “daughter”. Someone who particularly cared could have noticed that those similarities did not extend to Phoenecian, Egyptian and Aramaic (or even that Phoenecian, Egyptian and Aramaic were similar). The Greeks did not particularly care.