Can you have two identical passports?

I'm an American expat living in Europe (primarily Germany) and one of the most annoying laws there's that I have to have my passport on me at all times. After a few years, the thing ends up all bent and mangled up, and hard to scan at passports.

Even worse, a week ago, I was near a swimming pool when a fight suddenly broke out, and someone was shoved hard and fell into me--which caused me to fall in the pool and ruin my passport.

Is it possible to order two identical passports--one for carrying around in public for identification purposes and the other to keep at home for flying so I can give something presentable to the immigration agents at the airports?

No you can't because they don't want to ever take the chance that you could give it to someone else. I suppose you could just say you lost it and get a new one, but you would have to remember that the lost one would come up as stolen if it was ever checked beyond a visual. Realistically though you have to ask how much you are really getting it checked to carry it with you all the time despite the law. You could always get a metal case for it or just hide\lock it in your car, so it would never be that far. Otherwise I might look into seeing what type of German ID's you could apply for.

No. They do not issue duplicate passports. You'll just have to take better care of the one you have. Or order a replacement if yours gets so damaged that it isn't usable.

No. They will not knowingly issue you 2 passports. And it's specifically against the law.

You should invest in a quality passport cover. Like a leather one.

Possible, yes. I'm not sure how difficult. I used to work with people who had two so that they could travel to countries that ban people who have been to certain other countries.

No you can't, thats illegal
for example, you could be deported from one country and
still enter it again on another passport
better get a good passport cover to protect it

No, you can't

You may want to apply for a US passport card. It comes laminated (i.e. Water resistant) and fits in your wallet. See link.

There are differences between the card vs. Book. See link.

Here is a FAQ on the Passport Card for your review:

On a side note, please get your passport book replaced at your nearest convenience. If it is in as tough shape as you say, you may be denied entry into a country because of its condition.

There's no reason why not. Unless the USA specifically bans it.

This quite often used to be done for travellers in the Middle East because Arab countries won't admit anyone with an Israeli stamp in their passport (though the other way around this is to get the Israeli immigration officer to just stamp a piece of paper instead).

One thing you can do as a US citizen, and I don't know of any other country that has this, is you can have a passport card as well and carry that around. Of course that's not a full passport that would get you into Europe but it's good ID. Certainly European countries that require their citizens to have a national ID card will understand it.

You should consult an immigration attorney. I think in most cases it is not allowed

Of course not.