I _think_ those things are disconnected. If you stay more than 6 month + 1 days in Germany, I think it becomes your primary tax country and you fall into the German social system (for good or bad). But really, just guesswork. Ask someone :-)

If you are contracting for multiple clients, you should probably be cool. The thing which is problematic is if you only work for a single client (the mentioned "Scheinselbstständigkeit" - your claim to be self employed, but you really aren't). In this case Germany really just wants that you are regularly employed by that client company. (the reason is that this was commonly abused to force cheap labour into self employments, so that the employers also don't have to pay gov insurances and work around a whole lot of other laws ...)

Before Germany had the concept of UG we only had GmbH. For a GmbH you need to bank at least 12.500 EUR. Quite a sum if you wanted to start a business. So it was better to create a Limited in the UK and work in Germany. That construct was totally legal, but not really cheap since all the paperwork was for the UK and you ended up paying someone who knew what to do. The German government then created the UG. At grants you liability like the GmbH but you need only 1 EUR to start with.

Without being able to contribute to your question: in hindsight of Brexit (UK will leave the EU) this might not be possible (as easy?) as in the past anymore.

Freedom of movement is still in effect until the end of October, as for after that time the visa/residency question is up in the air but there's an extremely good chance residency of some form will be offered to British citizens who are already established in Germany.

As for the company being incorporated in what will become a third country, from my research I can't see any reason why that will fall afoul of any regulations (as long as everything is properly reported to the authorities).

I think the "only" real change is that he will need a work visa, the other aspects should remain the same. A EU citizen can freely choose his workplace in the EU (which is a reason why the British voted exit, they specifically didn't want that).

Thankfully freedom of movement is still in effect until the end of October. So no visa's required just yet. As for residency after the brexit date that's completely in the air but I would rather be already inside germany than outside.