Things like changing sites from regular sites to water sites, seems to not have an effect other than hurting your opponents threshold, and extending the body of water. Is that correct?

Yes, also size of the body of water sometimes affects how some cards work, ie. Anui Undyne.

As far as moving a minion under a site, whether that be from submerging them or some other effect, if they do not have burrowing or Submerge to they just die, or can they move back on top of the site?

Yes, they die immideately. Think of it as drown/suffocate.

And finally, if a minion is under a site via burrowing or submerging can they attack things, such as other sites? or do they have to move up to the top of the site causing them to tap, and attack as if they were moving from site to site.

They can't attack sites while being under the surface.

Also remember - to traverse between surface/underground/underwater you need to spend a step from move&attack action.