Yes. If you don't get enough sleep, you are less able to cope with stress.
Yes. Other people are like that. Even NTs. Ever heard of someone being "grumpy" because they didn't get enough sleep? Same thing.
Yes. Lack of sleep impairs your motor, cognitive and emotional functions. It also impairs the immune system, cell regeneration, the balances and cyclic restorations of various biochemicals, cycles of various hormones, metabolism, GI function, liver function and the body's ability to maintain proper weight (yes, less sleep can make you fatter).
As an Aspie, yes, if I don't get enough sleep, I am more sensitive to everything. I am also more prone to migraines, getting sick, having an allergy flare-up or having GI issues. I generally need about 9 hours of sleep a day. I need a good 7-8 hours straight plus a nap or two during the day.