Because that will fail to detect a program that halts in X+1 time. The problem isn’t to detect if a program that halts halts, the problem is to generally create an algorithm that will guarantee that the analyzed program will always halt given an infinite time running on an infinite computer.
Correct, the problem for Trump is under our legal system Juries are finders of fact. Trump can argue jury instructions were wrong or certain evidence shouldn’t have been allowed in, but even then the higher courts will determine if it is reasonable to conclude that absent that evidence, could a reasonable jury still have found the verdict. It is an incredibly high bar which is why most appeals fail even for people that we all likely agree were found guilty inappropriately.