Depending on where you own land in the US - strict covenants can regulate use of the land and buildings. Building code alone can be an expensive nightmare.

There is no actual double taxation between Germany and US but an income reporting system is in place. US residents have to file annual tax returns no matter where they reside and what their income is.

Contrary to common believe sale and ownership of firearms is tightly monitored. Consumers generally do not know a lot about reporting and back ground checks. Amongst others sale/ownership of certain firarms is prohibited to legal residents which are non-citizens. Some states require a permit with formal training to own a gun others are more lenient. Consider the difference longarm versus handgun - again different rules apply.
Some states consider a car part of a residence thus guns in the glove compartment are not considered "concealed". Check the small print - gun and amunition have to be seperate.

Yes - AK issues royalties to its legal residents after one year of permanent physical residency.