Should I post this in linguistics?

This sub is actually preferred for these kinds of questions: there are several historians of linguistics, as well as classicists, here. I'll let them jump in here, but meanwhile, there have been posts in here that may be useful.

how did we discover or "figure out" Caesar is pronounced with with a hard C rather than a soft C

Check out this classic /r/AskHistorians comment by /u/thatfool, in which they include a few explanations on "how we know", as well as providing several source citations.

• Original pronunciation of "Ceasar"?

how we discover the proper pronunciation of words from dead languages

It would help focus the discussion if you could specify which language(s) you're interested in. Old English? Latin? Sumerian? Old Norse? Ancient Chinese? Mayan? Ancient Egyptian? Here's a recent post on the latter; follow the last link to a post linking to a pile more:

• How do we know how to pronounce the names of pharaohs and other ancient Egyptian things?

if you have follow-up questions on any locked posts, just ask them here; page the relevant user by including their username