I have only had to make a claim against the AmEx coverage once, so I cannot answer all of your questions with certainty. That said, I am cautiously confident that:
- most rentals in Europe are covered. AmEx will not cover rentals in the following countries: Australia, Ireland, Israel, Italy, Jamaica, and New Zealand.
- car theft is covered.

AmEx's plan does not cover damage caused to other cars, and it proved to be a total pain to get AmEx to cover the loss of use fee that the car company charged. AmEx said that they would pay it if the car company provided documentation that there had lost revenue from having the car out of service, however the car company would not provide it. AmEx advised me to not pay that fee, however after the car company sent the account to collections, I got sick of the whole ordeal, caved, and paid it.

This page has information on AmEx's program.