It's perfectly fine to leave it running over-night, i do it all the time and i have a much much older system, no problems here, but do make sure to give the cpu some time to cool off once you're done with the overnight work(trust me, your pc will appreciate the rest)
i dont think its healthy, but then again its gonna die in like 5 years, its just like making your computer smoke, its not that good for it but itl die after a looooooong time
No problem at all. I do it sometime because I'm downloading a whole mess of stuff and they take awhile to finish. Other than that, I shut it down daily before going to bed.