Agreed, except that Ireland en England are part of Europe.
Also (and I'm not sure on this part) in The Netherlands we have WvSr aka Sr (Wetboek van Stafrecht, criminal law) and there's privaatrecht (aka burgerlijk recht, civiel recht). Subpoenas would be vordering(srecht). Government issue these as well, but it seems to fall under civil law.
Yes, there is a civil/criminal divide, this is not so much related to being civil/common law
(and just because this is HN, see the graph at the bottom of the page for a French example - though they call it civil and penal jurisdiction https://cours.unjf.fr/repository/coursefilearea/file.php/105... )
There absolutely is in many European countries. The divide is just along different lines than in US.
https://www-librededroit-fr.translate.goog/quelle-est-la-dif...
In Europe, police usually have a right to request information from companies and people. This is codifed into law, there's not necessarily any legal procedure for how it needs to happen.
There are some standards on how inter-country information is requested.
https://en.wikipedia.org/wiki/Civil_law_(legal_system)