Alright, let's break this down slowly:
Courts ruled that nobody's proven they weren't legal. OK, do you understand that bit? Oh, no, hold it, I'm aware you're in denial about that fact - you've made that very clear. I'm asking if you just understand what that means.
And since the burden of proof is on the accuser - so, that means, in American jurisprudence,
we go by whether you can prove that a vote was illegal. Nobody has to prove that votes were legal; someone tries to prove that a vote was illegal and then the other side has to prove that there's a problem with their proof. Same reason cops can't bust into your home demanding you prove that you didn't kill Jimmy Hoffa; they have to prove that you did first.
All vote counts were good. Pretty much, the absence of proof of a crime is taken as proof of an absence of crime. You didn't prove illegality, therefore they were legal.
Any further questions, refer to the court rulings. There are 60 of them. OK, so that means, basically, read what the judges wrote. They write very clearly and very directly about what they were thinking when they threw these cases out - exactly because they know they'll be scrutinized as to whether they were following the law as opposed to following a political desire. If you read them, any further questions you might have will be answered in those documents.