They are offering me 18.7Zł(with raises every few months) net per lesson with 60-100 lessons in the low season or 110-150 lessons a month in the high season. The thing I am worried about is the rate of pay because I'm not sure it's enough to live on my own in my own apartment in Katowice.
Berlitz is NOTORIOUSLY cheap. The normal rate at better schools is more than double that, even triple, so what they are offering is just plain atrocious. Forget about it and look elsewhere.
As a rule, though, there are not to many opportunities for non-EU citizens. It's much easier to hire people from the UK and Ireland. You'd be lucky to find work in the lousier schools like Callan, Avalon or Direct Method schools and Berlitz, where the wages are low and working conditions are poor.
Sorry, but the opportunities for teaching in Poland for unqualified non-EU citizens have long dried up. That ship has long sailed. Even for EU citizens, it is less attractive because wages have stagnated while the cost of living has continued to rise.
I may be able to stay with relatives rent free possibly
Probably not. You will almost certainly be expected to contribute for your room and board. About 1500 PLN would be fair. Poles do not abide parasites or freeloaders.
are these wages enough to live off of in this city?
Not by a long shot.