that depends... turning off your screensaver will slightly increase hashrate, in case you are using a nice gfx-card for hashing, that "slightly " decrease could be in the range of about multiple cpu's power, on the other hand turning off your monitor, could save 10% or more of your costly spent electric power, so better deactivate screensaver and monitor for mining purposes
running a pc 24/7 doesnt actually damaging your hardware, but you have increased wear of moving parts of course, ie. hard drives and fans. think about installing solid state hard drives and watercooling for your gfx-card and or cpu if you are worried about that, or if you could get hands on it, a heatpipe passive cooling solution, with no moving parts at all, but could be expensive
btw i did run my pc 24/7 for three years now, before i began to mine, with no damage exept my gfx-card that was killed by last summers heat wave because i missed to clean it from dust ^^
jm2p Zeph