Per Diems are paid monthly. If you're not Gateway'd in the UK or Denmark, they are untaxed (as far as I know) and €70/day.
As for PT v DE tax? That's for someone else to answer.
I'm in the UK and taxed there. (ouch).
I *think* for now, you'll be taxed in PT and pay your Social Security in Germany. I'll let someone who knows more accurately answer.
The question does come up fairly frequently so if you haven't, scroll back and see if it has been. (Or check out older threads from 2021 or 2018).