1. do i need any special permit for buying apartment?
2. if i go to another country out of EU, on what basis is property still in my name?
Of course. It's your property.
3. can i give this property on rent to any other person?
4. can i hold a polish bank account when im not living in this country but based on the property i have in poland?
In some banks you can open account, but you must visit them in person.
5. how is the tax calculated for such income?