Q: Are there alternative antioxidants?
A: No, otherwise wine makers would use them!
Q: Will higher ABV will protect the wine from [microbial] spoilage?
A: To some extent, yes, but not entirely.
Q: Can cheap wine cause headaches?
A: Yes (OK, well, probably, since the science is not fully understood)! Poor quality fermentation produces many toxins besides ethanol such as methanol, other fusels, acetaldehyde, sulfide, other cogeners, etc.
A: I'm more concerned that the cleaning agents used are in the wine.
Q: What are you talking about? Fining agents are non-toxic.
Q: Would Pasteurizing in the bottle like in this thread work for wines or meads?
Sniped by @TechFanMD
A: Oxygen is enemy #1 of wine. You could steal a page from the brewer's playbook and use 22oz beer bottles (made to contain pressure unlike normal wine bottles, but similar in size to wine bottles), bottle carbonate with a measured amount of priming sugar/must (the yeast will consume some oxygen), and use oxygen-absorbing bottle caps. Wine packaged this way will probably be good for at least several months.
There will be sediment/lees in the bottle.
BTW, when you heat pasteurize your cider, those aromatics you smell are then lost for good. But if you don't mind then it's all good.
Hope this helps
Chemicals used to clean vessels.