I don't actually think either of those things are all that hard, certainly it's a gray area until this actually happens but I think AI generation is not all that different from any other copyright situation. Even with regular copyright cases you don't need to prove "how" the copying occurred to show copyright infringement, rather you just have to show that it's the likely explanation (to the level of some standard). Point being, you potentially don't need to prove anything about the AI training as long as you can show that the AI's result is clearly identifiable as your work and is extremely unlikely to be generated any other way.
Ex. CoPilot can insert whole blocks of code with comments and variable names from copyrighted code, if those aspects are sufficiently unique then it's extremely unlikely to be produced any way other than coming from your code. If the code isn't a perfect copy then it's trickier, but that's also the case if I copy your code and remove all the comments, so it's still not all that different from the current status quo.
The bigger question is who gets sued, but I can't imagine any AI company actually making claims about the copyright status of the output of their AI, so it's probably on you for using it.
Ex. CoPilot can insert whole blocks of code with comments and variable names from copyrighted code, if those aspects are sufficiently unique then it's extremely unlikely to be produced any way other than coming from your code. If the code isn't a perfect copy then it's trickier, but that's also the case if I copy your code and remove all the comments, so it's still not all that different from the current status quo.
The bigger question is who gets sued, but I can't imagine any AI company actually making claims about the copyright status of the output of their AI, so it's probably on you for using it.