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installing it back
It means the same as in, for example, installing a kitchen. You have a bunch of files/materials which you ready to be used.
It might not be compatible for your type of computer or you might not have enough disc space.
Starting or restarting a computer.
A new harddisk will have no files on it. If you mean filesystem, it depends on the manufacturer.
If you mean - to use a USB drive to boot up your computer instead of installing the software on the computer's hard-drive - theoretically, yes. HOWEVER - if your USB stick went faulty or you lost it - you wouldn't be able to use your computer !
A hard disk drive is used to store data. That data includes the programs you use. When someone says they are installing something on their computer, they usually mean they are installing it to their hard drive, which is located inside their computer. In most situations, a hard drive is what loads the operating system so you can use your PC. If it fails, you will not be able to fully boot your PC.
Installing the program to your hard drive
I'm sorry, but I don't really understand this question. I'm not sure what is meant by "computer top". If you mean a laptop shell, you can find them starting around the $30 range.
Once you see your computer's desktop, your computer has already booted. However, this does not mean that all of your computers programs have already loaded. For some time after your computer has booted there are other programs that are still starting up. If you try to play a video game while these programs are still starting your computer will run very slow since it is trying to both run your game and start these programs at the same time.
If you mean installing "The Sims" on your computer, the instructions should be self-explanatory. Merely pop in the disk into your CD/DVD-ROM drive and use the Autoplay function. If you mean OS simulator software, or more accurately, emulation software, then you would have to pursue buying VMWare or similar software to emulate older environments in order to play video games. Be careful if you wish to do this, though.
it mean there is a hacker in your computer