Export coins from Germany to places outside of EU?
Depends: If bought in a local coin store or at a coin fair from an official dealer, in most cases “no problem”.*
If you plan to steal from a museum or dig up an ancient coin in a field => always illegal
If you buy from a shady guy that might have sourced the coins in a museum or dug up a field => illegal
If you buy legit but plan to export to a country currently under sanctions prohibiting export of valuable coins (e.g. russia) => illegal
* For single coins older than 50 years and also worth more than 50000 Euro a piece you need a special permission for export (older than 50 years and worth under 50000 Euro a piece is no problem, no permit needed here. Export of an entire collection worth >50000 Euro combined if they have numismatic value (it's a bit vague what that is, but a collection of German States could fall under this, probably more of a money laundering prevention…) also needs a permit. Should be no problem to get one unless you plan on exporting something rather unique that could be a museum exhibit.
So unless you are super rich and plan on exceeding the 50000 Euro limit, you are good to go without any permits or problems, as long as you don't do shady deals acquiring stolen stuff.
