George, Andy, Tommy, etc are all constructs summoned from the Lab 8 weapons arsenal and modified by Peacock's artificial parasite Avery. No one is quite sure how she's bringing them to life as the Avery system is not supposed to do that. Peacock's other parasite, the Argus System is what lets her see and replaces her arms (and possibly legs).
Avery is possibly a remote parasite, but because he's artificial there's all sort of rules that may not apply.
Krieg, Hungern and Vice-Versa are all living weapons. They are not sentient and are not bonded to their hosts, though generally only certain people are able to use them which is why Cerebella has Vice-Versa and not a more serious Medici Mob thug.
The Life Gem is unexplained. I'm guessing it's just a gem with magic powers.
Yes, naturally occurring parasites are always sentient.
The nature of parasites has not been explained. Some just seem to be more powerful than others.
When Samson eats something it's probably considered brain food.
Really though, when Samson eats Filia puts on weight, so their digestive systems are linked.
Parasites are extremely long lived, though it's never said if they are actually immortal. Sekhmet seems to think she is anyway.
Leviathan was in Squigly's dad's shoulder. Parasites can exist without hosts for short periods of time, but they will die unless they bond with someone. If a parasite is removed from a host, the host immediately dies.
Buer and Gae Bolga are artificial parasites so the rules that govern regular ones don't apply. Some seem to be sentient and some are not. Skullgirl blood is skullgirl blood and just seems to boost Painwheel's power in some way. Yes, the one Painwheel wants out of her head is Brain Drain. No he's not a parasite, he's the only surviving member of the Lab's psychic soldier program.
There are basically no details available on any part of the Trinity. Stay tuned for Eliza's story mode which is apparently stuffed with lore!
Panzerfaust's tank is apparently just a mechanical tank arm built and maintained by Roxy. No specifics were mentioned about this though.
tll;dr Go read the wikis. All this info is in there :P