Taking a course while dating the TA
This really depends on the country, the institute, and its specific rules. If you're concerned it would be worth speaking to the TA about it as they would be 1) more aware of the rules and 2) probably more likely to suffer if it goes wrong.

I know in my institution in England, I was told when training to be a TA that it's fine as long as you're not directly marking their work. The advice was you can go to the course leader and say 'I can't mark the work of student X because we're dating'. But I've heard in the US generally rules are a bit stricter. And I'm sure rules differ across the UK too.

I'd say in any case, transparency is the best option here. If you try to keep it secret to avoid consequences, the consequences may end up more severe.