The word powinien is a former adjective that assumed the role of a verb hundreds years ago, and it merged with być, therefore it takes the same ending as jest. It's the one of two Polish defective verbs that conjugate by persons (the other is winien and it's a less popular synonym of powinien – don't confuse it with an ordinary adjective winien/winny), and there are no words other than those two that follow this pattern.
masculine personal plural:
Past tense (althought you can use the previous forms to refer to the past as well):
Conditional mood (rarely used):
There's no future tense or any other forms.
Hi, I do not know formal rules, but as a native speaker I can give you small hint: "powinieneś" (should) is related with word "powinność" - duty.
My guess would be that it evolved into „ś” because of preceding syllable being soft. It just sounds strange to me going from soft „ni” to „sz” at the end.
I was referring to -nie- before that. It's just strange to me, but vytah's explanation is probably closer to truth.
Shouldn't the english translation be rather "you are not obligated to be here"?
No, it's good now. Sometimes the negative meanings of some words might not make intuitive sense for somebody coming from a different language. In Poland for example people learning English might at first be surprised with the meaning of "musn't", which they might expect to be closer in meaning to "don't have to".