She seems like a very sincere person
1,000 PLN in gas per month
I'm sure she's sincere, but she's probably jumping for joy if you're paying 1000 for the gas bill. I suspect this includes gas to heat the water, but even so, It seems a lot.
Supposedly, according to the realtor, who speak English, I will get money back some time in the spring time if I have used less than 1,000 PLN worth of gas every month
According to time-honoured rental tradition, the key word is 'supposedly'. Who are you paying the money to?
The apartment is 84 square meters, perfect location for me where I can walk to school and hospital.
Seems great by Warsaw standards.
There is vinyl flooring everywhere except the living room and bathroom
Unusual in Poland.
which would lead me to believe it's done poorly..
Not unusual in Poland.
I strongly suspect, since there's a realtor that you have a Polish-language contract. Maybe you could call the realtor. Also, you'll need to be registered in the flat (zameldowanie). If you aren't, then it's a fairly good (though not 100%) sign that you're renting the flat on the black economy. This means they can't really do much if you leave. They will however make a lot of noise, and you should consider whether it's worth the hassle etc.
Personally I would have a look on Gumtree to check out what you could be getting in Bydgoszcz for the same money or less. I suspect you might find somewhere smaller and more modern in a block for that price. It would probably have district heating and be very warm indeed.
What do you mean?
Of course then they can sue me in another lawsuit about the legality of my claim.