I disagree on almost all those points.
Why do you think 25% voted, based on what evidence? For that matter why do you think people are registering illegally and voting anyway??? Its hard enough to get legal voters to actually vote, what would motivate individuals to risk breaking the law and voting? Unless there is some organized movement, the effect of their individual vote is tiny? Why would they take the risk and make the effort?
Imagine John Smith is here illegally. Why would he take a chance of being noticed and deported in order to vote? It makes no sense. Much more likely he ended up getting automatically registered.
I've voted for many years and I'm not concerned. I've seen not evidence that this is a big problem. Why spend my tax dollars fixing it?
States mange their own elections and none are claiming a problem with massive illegal voting.
So, there is a law that says you have to prove that you are a citizen before you can register to vote.
There is an automatic registration to vote through driver's license procurement.
Ignorance of the law is not a defense.
If you are not a citizen, you would want to say that you would prefer not to be registered to vote.
How would they know you aren't a citizen? Because you said you don't want to be registered? Makes no sense. it isn't illegal to refuse to vote.
All the rest of your questions don't need answered. This is the only situation there is, that needs addressed.
Who is responsible? The state which registered those foreigners or the foreigner?
It's the foreigner's fault, since ignorance of the law is not a defense. i.e.: I didn't know it was illegal to kill that man. Nope, doesn't work, you have to stand trial and be punished, if convicted.
Get it now?
If, for example, Oregon registered foreigners to vote illegally, it will have to be fixed. They will have to find them through all those licenses. They will have to change the system.
Is it the federal government's money that should be spent to fix Oregon's mistakes?
Nope, it's up to Oregon to fix them and use Oregon taxpayer dollars.