Question 1: No it's not possible to transplant an eye from an animal to a human, tissue rejection would be horribly swift & severe.
Howsoever, with a little round or two of musical organs it's plausible, throw in some handwavium & it's definitely possible.
Here's how, based in the main on ideas from this question of mine.
Step one: grow a pig with a few of your cells & those of the donor animal of the organ you want (in your case an eye) introduced into the foetus in vitro shortly before it's immune system is calibrated.
The pig will develop with an immune system that recognizes both your cells, the eye donors & its cells as its own.
Step two: allow pig to grow to maturity.
Step three: remove all of your own organs & tissues associated with your immune system.
This won't be pleasant.
Step four: replace with the pigs, this will kill the pig of course.
You now have an immune system that recognises your own cells, those of the pig, & the eye donors as its own, no tissue rejection.
Step five: transplant eye & job done, relax & have some bacon sandwiches from leftover pig.
The big issue remaining is the severed nerve tissue you've spliced together, nerve tissue tends not to grow back.
Accept that it does sometimes, there are people who have had arm transplants & the like who have gone on to regain use & functionality of their new arm & digits over time.
So just throw in a little handwavium (you may need less than you might think here) & stem cells slathered liberally on the spliced nerves to promote growth, results won't be immediate of course.
Now for the big "But, this won't work", the tricks above should work well enough for xeno transplants from other mammals & perhaps even reptiles but something like a mantis shrimp that doesn't even use blood like ours is just much too different in its biology, individual cells wouldn't thrive transplanted as detailed (the cell chemistry is all wrong) so organs won't either.
Think of it like putting a salt water fish in a fresh water pond, the environment (your body) is just wrong for it (a crustaceans organ) & it will die with or without an immune response.
But stick to animals with the same blood & cell chemistry as our own & you'll be golden, plenty of mammals & such out there with eyes that do more or something different to ours.
Question 2: I have no idea, someone else will have to answer that, but I strongly suspect full functionality is unlikely for transplants to adult humans of eyes with differing properties to human eyes, though transplants to infants, the younger the better, will likely produce better results, not immediately but over time, as the developing brain is amazingly plastic.