I was wondering will my Pi be damaged if I never shut it down/if I just keep it running indefinitely?
Hi. I have RPi 1 model B and B+ hardware running about 29 months and I have RPi 2 hardware that has been running 13 months. Out of a total of 10 RPIs operating pretty much continuously for a year or more, I have had no failures, but one scare which turned out to be the power supply, not the RPi. None of them use any aftermarket heatsinks or fans. Half of my Pis are in the little plastic cases https://www.adafruit.com/products/1997
you can buy, half are in larger plastic enclosures. All are operating indoors at normal room temperature for humans, no unusual or special environmental conditions.