Yes, schools can be terrible for that, although its not always malicious sometimes they just don't know about licence conversions!
You need to look at
Title 14 Part 61 of the CFR, available on the GPO site
If you go down to Subparts E and F you will see the requirements for both PPL and CPL
Training can be conducted overseas by non FAA CFIs if you look at Part 61.41 in that link I gave you. Therefore if you meet all the requirements for PPL/CPL issue you don't have to redo the whole syllabus.
"all your hours count and you need only do suficient to pass the skills test, oral exam and writen " is about the right one. The schools themselves will often exam you, there is none of this UK CAA "passing of a skills test gives you the right to respectfully apply for a licence". The examiner will check your paperwork before you go fly, and if you pass the checkride he will issue you a temporary licence there and then, pending the later arrival of the official one from the FAA.