I did a condensed (2-week) IR as part of a (very) condensed 6-week PPL / IR / CPL / Multi course.
A few thoughts:
Doing an IR in 2 weeks was very, very tough. It would be much more do-able if you have some previous experience (eg an IR(R)). You will need to allow some extra time in your schedule in case of weather or the aircraft going tech. If I was to do it again I wouldn't aim for two weeks .....
Under FAA rules if you are qualified to fly the aircraft (ie you have an FAA Airman Certificate) and the flight is done under flight rules you are qualified to fly under (eg VFR in this case) and you are flying the aircraft then you can log PIC for the flight - so in other words your dual IR flight training, if flown VFR, can be logged as PIC. However this time would count as "dual" from an EASA point of view so wouldn't count towards P1 requirements for your EASA rating.
My very limited experience of IR training in the US vs IR training in Europe (I've only done one FAA IR and one EASA IR!) is that IR training in the US was very much geared towards private pilots flying clapped-out old aircraft around the place under IFR, whereas EASA training was geared more towards commercial pilots, so the emphasis was very different. 10 hours instrument training would typically be only 3 or 4 flights - there are plenty of experienced FAA Instrument pilots around who have done the existing EASA IR conversion route who took way more than the required 15 hours to convert. I'm sure there are schools around in Europe who offer courses more geared towards private pilots.