None of the rental companies in Europe will deal with third party insurer (such as American Express). But that doesn't mean you can't rely on the cover. This is for the excess / deductible - the car has to have base insurance purified by the vehicle owner.
It means that should you have "an event", the rental company will charge your card and you then reclaim that from your card insurer. There a level of faff and form filling to plough through but it works.
Yes, automatics are available, but they're a specific booking class and you need to specifically rent that. This may cost considerably more than the equivalent in manual (or it might not..... There is little rhyme or reason to price levels sometimes).
All rental companies in Europe are strict in damage control. I had the misfortune to scrape an alloy wheel on a hertz rental out of Munich a few months ago. The charge was €480 - which i reclaimed from my amex insurance cover.