An O1 Visa implies the "employee" is not staying in Germany, but coming to the US. Otherwise being a self-employed German and sending invoices for work done to the US company would be way less paperwork for all involved.

German labor laws do not concern Germans working in other juristictions for companies in those juristictions.

Germans file taxes based on their place of work. Although filing jointly with a married partner still remaining in Germany or having multiple employers and places of work in the same tax period where one of them is still in Germany might complicate things for that tax period, generally speaking, if you are not in Germany and not employed by a German company, you don't pay taxes in Germany and you are not affected by German labor laws.

There is no obligation to pay into any systems, but the person in question may want to do that voluntarily. Sometimes it is better to stay in the system or use the system, even if you pay out of your own pocket. That is basically what self-employed people do. But it does not concern the US employer, it's between the German and whatever system (health care, social security, artists have their own thing) the person is in and maybe wants to stay in.

An O1 Visa implies the "employee" is not staying in Germany, but coming to the US. Otherwise being a self-employed German and sending invoices for work done to the US company would be way less paperwork for all involved.

German labor laws do not concern Germans working in other jurisdictions for companies in those jurisdictions.

Germans file taxes based on their place of work. Although filing jointly with a married partner still remaining in Germany or having multiple employers and places of work in the same tax period where one of them is still in Germany might complicate things for that tax period, generally speaking, if you are not in Germany and not employed by a German company, you don't pay taxes in Germany and you are not affected by German labor laws.

There is no obligation to pay into any systems, but the person in question may want to do that voluntarily. Sometimes it is better to stay in the system or use the system, even if you pay out of your own pocket. That is basically what self-employed people do. But it does not concern the US employer, it's between the German and whatever system (health care, social security, artists have their own thing) the person is in and maybe wants to stay in.