Two issues here :
Conversion :
Less than 100 hours as pilot
Article 8 of Part FCL governs this which means an ATO must recommend the training plan to your Competent Authority which holds your medical records for the conversion which they can approve or deny.
I have not had any conversion requests of less than 15 hours training approved at PPL level. This may completely negate the cost savings of doing an FAA PPL.
Have you considered completing the EASA PPL in the USA -
European Flight Training Home - European Flight Training Florida Institute of Technology both have EASA approval to do this.
More than 100 hours as pilot
If your total hours exceed 100 hours then you can complete 2 written exams (Air Law and Human Performance) and just take the test. If you fail you will need to go to an ATO for training
Yes your hours in the USA count -
with the exception of "safety pilot" time. In the USA some schools sell hour building as two pilots flying at the same time to build hours. One pilot flies with reference to instruments whilst the other is safety pilot time. This is not recognised in Europe.
PIC whilst receiving dual
In the USA under FAA rules if you are qualified on category, class and type you may log PIC whilst under training (as does the instructor) In Europe as most training aircraft are certified single pilot there can only be one pilot in command (the instructor), you the student must log dual.