So dying to the flesh means not doing what your flesh wants, right?
To an extent. Your flesh wants to eat, but that's not necessarily a sin. So by denying the flesh you are denying evil fleshly desires such as unrighteous anger, fornication, lying, gossiping, adultery, murder, speeding, disobeying your parents, etc. etc.
But does this mean that I can also die to myself if I'm hungry and I resist eating something?
That is exactly what one does if they are engaged in a period of fasting. Especially if it is of any length of time. But for others skipping one meal would be a challenge.
But you wouldn't want to do that for long although it is possible. Your body needs food to continue its existence (of course I'm not telling you anything you didn't know already). But if one wanted to they could resist the body enough to kill it by not eating I'm sure.
Not a big expert on buddhists or any other non-Christian religion.
Some great advice that I was given was find and study the truth and the counterfeit will show itself immediately. No reason to study other religions in light of the Truth of Christianity.