Any advice for monthly cost of food?
If you cook almost exclusively at home, and stick to the Polish poor-folks' staples of potatoes, rice, pasta, bread, cabbage, carrots, onions, beans, pickles, apples, eggs, dairy products and tea with a little cheap pork, sausage, chicken or fish occasionally thrown in for protein, together with sundry household supplies and laundry done at home, you could theoretically get by on 400 PLN a month, as the bulk of students and young workers do.
But face it, you're probably not going to put up with a bland, monotonous and time-consuming diet like this for too long, and you're going to be spending substantially more than that, especially eating out three times a week (that will cost you 240 PLN at least in itself). Bank on 1000 PLN, and probably more if you drink coffee or tea in cafes, or soft drinks and snacks away from home.
That, together with your other living expenses, will exceed 2000 PLN if you manage to find a cheap student room.
Alcohol and nightlife can be very expensive indeed. Again, that depends on your tastes and how disciplined you are, but can easily exceed 1000 PLN in itself.
You still have travel and other entertainment expenses to consider, plus your phone and internet bills.
And then you have to take your airfare and visa costs into account.
Looks like you will have to chip in from your own savings to cover your expenses. How much depends on how monkish you are willing to live, but from the lifestyle you described above, you'll probably need at least 1000 PLN beyond the 2000 net you will be receiving.