It's not about patience or building character...I have been here a while and I do ok day to day.
It is about them not even knowing the rules and then me being punished as a result. They can't even tell you the full requirements...and then later they tell you to come again with some document they NEVER in writing, on a sign, or to your face told you about.
Okay, apologies for thinking you're a newcomer.
But my basic advice still stands. The problem is that _they_ are not sure what the rules are now and that makes Polish bureaucrats _very_ nervous. With Poland's entry into Schengen, the old system isn't really valid anymore but no new system has been put in place (and I know of no plans to put one in place).
When Polish bureaucrats know just what the rules are, they're much more confident about waving and/or bending them. When things are unclear they retreat to "Everything you've done is wrong" mode (so that they won't be held responsible in the face of regulations that eventually do show up).
It sucks that this has come up while you're trying to get your paperwork in order but I still think the best you can do is store up your patience and contain your rage (and never let them see the latter) and keep plugging away at it, smiling and thanking them for letting you know about the latest paperwork they've asked for.
If you're seeing the same people more than once, then that's good. Once they come to recognize you (and know you're not gonna be making nasty scenes) they'll be much more inclined for your paperwork to finally get through.
On work permits: From what I recall (this might be dated) foreigners don't need work permits to teach their native languages but this might depend on the level you're teaching at. Unversity level instructors definitely didn't need a permit a few years ago (when helping a co-worker jump through some hoops) but lower than that I'm not sure.
But again, Polish laws are almost always badly written (without thinking through all the consequences) and/or ambiguous. It's usually up to the local person in charge of how to interpret bad and/or ambiguous regulations.