Extended use of a pc shouldnt really slow it down unless you use a lot of different programs.
Each time you run a program and then close it you may find that it doesnt release all the memory thats been allocated to run that program. So if you open and then close down a lot of different programs you may find that your pc slows down. A reboot will release all the memory and start off again with the maximum available.
A power failure will definately crash your pc, whether it does any harm or not is hard to say. You would lose any unsaved data that you were working with at the time of the failure.
The actual physical damage to any components would be more likely to occur when the power was resumed and you may get a surge or a spike if your bios was set to resume after power failure.
Its always a good idea to have your pc plugged into a surge protector extension.
I hope this is helpful to you