Is a wedding in Las Vegas without self-initiation legally valid in Germany?

Hello everyone, we would like to get married in the USA and are looking for answers to important questions:

Getting married in the USA is not a problem: simply meet the requirements and receive a marriage certificate.

However, the marriage is not automatically recognized in Germany. A certified copy of the US marriage certificate and an apostille must be submitted. An apostille confirms that the marriage certificate is authentic.

With these documents, the marriage can then be recognized in Germany. Now the questions are:

So you could just do it that way, but in Germany, you'd never be married without taking the initiative. You could even have a bigamy, because the government doesn't check in which other countries you're married.

Of course, tax and legal advantages or disadvantages only become apparent after the marriage has been recognized in Germany. What if I get married abroad in August and have the marriage recognized in Germany in December? Does the tax advantage then apply for the entire year?

In a German marriage, you can agree on a name, separation of property, community of accrued gains, etc. Is this also done in Las Vegas, or does it have to be decided in Germany? After all, you would already be married under foreign law.

Does a foreign marriage, especially in the US, have any advantages under US law? You certainly won't be allowed to immigrate, and you won't get citizenship, but you might get other tax or tourism benefits?