I would say it's something like this:

Mieszkam w tym domu. = I live (reside; my home is) in this house.

Tygrys żyje w zoo. = The tiger lives [out its days] in the zoo.

Mieszkać I believe always refers to having a home, whereas żyć can mean what it does in this example, or it can mean 'to be alive'.

(In Finnish we have two separate verbs for 'live', just like Polish does; English can use the same verb for both, which makes it tricky.)

Sure, added.

Well, that translates very easily to "nieszczęśliwy".

Seems fine, added.