I should pick up a package from Temu for my father at the post office?
You need an official photo ID and (this barcode from Temu that the package has arrived somehow)
I have no idea about that
Can I pick up the package with my ID?
Or am I not allowed to do that in principle?
The package is/was delivered to the post office.
Sure, but you also need to bring a power of attorney from your father.
You need a power of attorney from your father so that he can authorize you to pick it up, then it will work.
Actually, he has to do it personally, he should write you a power of attorney
It's called power of attorney.