Any device that emits RF is subject to the FCC. Since there are trace RFs coming from the CPU, it is under their review. Many can get a class waiver based on the CPU if the CPU manufacturer has already gone through the process. WiFi and Bluetooth are both under their authority to review.
No, the FCC has authority only in the USA and USA controlled areas like the Virgin Islands and American Somoa. The EU has its own set of rules that differ from the FCC. Canada and Mexico have their own sets of rules too although they are closer to the FCC's rules than the EU rules.