Two different issues:
1. Paper licences: No longer valid for any certificate. You will need to contact the FAA and request a plastic one. If you have a 61.75 cert then any changes to your underlying foreign licence, change of address etc will require a reissue of the whole thing ie foreign licence confirmation from the issuing Authority. Otherwise it's a simple replacement.
2. BFR: A current BFR is mandatory to exercise the privileges a US certificate. There are a few other checkrides/flight tests events that meet the BFR requirement but the general rule is a flight review within the last two years.
The key language in the FARs is that it must be with an authorised instructor. The only authorised instructors are those that hold FAA instructor ratings - hence why similar flights done with a foreign instructor don't count. Unless the instructor also holds an FAA instructor rating, of course - but then it would be with an FAA instructor. Geddit?