
ASE is the National Institute for Automotive Service Excellence. An ASE certified mechanic has been instructed and tested on how to perform maintenance on a vehicle. There are different areas of specialization for ASE certifications for different systems on a car. ASE certified mechanics aren't necessarily better mechanics but they take the job seriously enough to take the classes and tests required to become certified.
After market denotes a part produced for the vehicle by a company other than the original manufacturer e.g.
A loaner car may be part of your collision coverage, but it is worth asking the question.