Mój sąsiad szuka żony.
Discription says sąsiad is genitive, of course it must be nominative here and wiktionary.org says genitive would be sąsiada. Maybe Discription is wrong here?
And it still says "Genitive" in the pop-up. You could report it.
It can take some time to implement though.
Can rolnik have a pejorative undertone?
Not really, it's a profession.
Why can't i use contraction My neighbor's a farmer?
It should work - I suggest you report it (but it might get fixed anyway :-) now).