I think that there are several things at play here. The first is how your son feels about all this - I know you had issues last year with organization... is he putting forth the effort in these classes that they need? Does he really want to be in them?
As far as math, I don't see ANY problem with you being involved. He's a freshman in HS, not college, and I would expect he'd still need guidance. Many college students like studying with a partner. I think it is a question of whether you are the one pushing on this or he is (does he ask for your help?). I think you absolutely should go in and sit down with the teacher and your son and look at the tests. That is not uncommon at all at our HS (our kids also can't bring home tests). For all you know, it's a lot of stupid mistakes, not really a lack of understanding. And if you've been helping him with studying, you're probably in a really good position to evaluate how the tests relate to what they've been learning. I don't think that it's a bad idea to have tests be an extension, but there has to be some relation to what they've been doing in class.
I'm surprised his school is dropping him levels so quickly. At our HS, that's nearly impossible because many of the honors/non-honors classes use different books. It's pretty much unheard of to change levels after the first 12 days. And I think many kids are a bit overwhelmed the first semester of HS (although I have to admit, as the parent of a kid who will be doing honors AlgII/Trig, Honors Bio, Honors Eng and AP World next year, you are scaring me a bit ;)).
Have you read his English essays? If he has been doing literary analysis since 4th grade, I think you need to figure out why he's struggling so much. At our school, kids from both the regular and gifted programs go into honors Eng in HS and the HS honors class definitely starts out providing step-by-step instruction (usually boring to the kids who were in the gifted class). That's a really important skill, and with such a gap between the honors and regular classes at your school, you want to make sure he's not going to to go to regular and just coast along and not learn anything. Which would bring me back to - is it lack of ability or lack of effort on his part? Could he just be feeling overwhelmed and want to retreat back to regular classes because he knows it will be easy? I don't think kids need to be in all honors, but you want him working at a level that is interesting and challenging to him.
Finally, congrats on all your work getting him into the honors science -that seems to be going the best of everything, so you should feel great that you got him in the right class!!