1/2. Yep, no doubt. Though it also has proven benefit for angina (again, of course unlikely) and PE (likelier, but still unlikely, though we don't have a full history).
http://circ.ahajournals.org/content/125/10/e439.full.pdf Unfortunately, this:
http://smchealth.org/sites/default/files/docs/388374270Aspirin_in_ChestPain_Update.pdf is the best source I can find re aspirin in flu-like chest pain, but I can't find anything that suggests against it either.
3. Probably not, but I'd say the risk of 75mg of aspirin (what most people will have) is pretty low, and it at least has a chance of helping.
4. Gastritis? What makes you think that? That's not normally associated with chest pain, surely? Would flu (or similar) not fit better?
5. I would hope people read the contraindications before taking medication (and I would imagine they would've been told they can't have aspirin when they got the asthma diagnosis).