1. Appartment rental for 2 Rooms, furnished in Gdansk Area.
Have a look here. Most look between 1500 and 2000. There will also be bills (gas, water, electric, internet, 300-400 on top.
With a Net take home, of 16000 PLN / month, how much can i save - considering once / twice month eat out and entertainment , utilities, internet, etc on a broad scale. How much can i potentially save ?
Up to 10,000. You will live very comfortably on 6000 and many people manage to save on just that.
3. Is buying a used car and maintaining it a costly proposition ? Or should I stick to public transport.
It's a nuisance but possible. People in Poland don't like buying second-hand cars, and it would be difficult (or impossible) to get credit for a longer period than your residence permit. Public transport in Gdansk is excellent however one possibility would be to speak to your company about leasing.