Of course you can use it for how many days you want (however, to improve the performance of the PC, we should give some time off). And, its better to enable the screensaver option.
The speed of computers also has a very large range. Computers have become indispensable in today's world
Mine are left on for days on end and very rarely do i re-boot them,as i gone over to mostly Dell computers these days these are so ultra reliable you can leave them switched on all the time.
Of course you can. I have kept my computer for one week without turning it off but due to load shading problem I have kept my PC on stand by mode which is not turning off.
Yes. But for how long depends on your operating system. Linux and Apple systems can generally run for months without a problem. Windows ( also depending on what programs you've installed ) tends to develop memory leaks. What this means is that it forgets where it put stuff, and so you have less and less memory to use, and run out of space until you stat getting crytical memory issues. This is usually a good time for a reboot. If you need the thing running 24/7 - as a media server for example - best bet is to go with Linux. Ubuntu's good if you're starting, or Zentyal for a good file server/firewall box.
Yes, you can have it on continuously but make sure that the fans are working properly and there's adequate ventilation.
Yes you can use 24/7 but make sure your PC don't any overheating issue use it with proper cooling system.
You can use it as long you can, But if your not that much loaded work then i personally suggest you to keep it off if not in work... I think it may be harm to your board components cause its much heated though. A fan cant handle that much heat.. I can say that if you going to work that much long then you need to apply cooler paste on your processor at out side...
I think it will not be a problem because even server computers are always ON. However, the computer's performance may be not good if you keep switch on the computer for days. A reboot or some shutdown will improve the performance of the computer again.