The question pretty much says it all. I had a problem with RAM and bought new ones. Theoretically, what else could cause RAM problems that can be avoided?
No. Shut it off as often as you like, whenever you like, should NEVER affect the RAM.
Avoid static discharge while handing RAM outside the computer. Avoid using the computer as a lighting rod. Don't install or remove RAM with the power on.
Good RAM is trouble-free, or warranteed. Cheesy/counterfeit/whatever RAM perhaps less so, but even there it's usually troublefree (ie, I have seen very little to support paying 10X the price for RAM, but don't mind paying a few dollars more for a known brand/vendor, given the choice)
No, turning the computer off while the computer is running will not damage RAM.
However, it can corrupt your data. Any unwritten data in RAM or cache will not get written to disk and this can cause a loss of data.