Is there a software that allows a person to see everything that I do with my computer in real time like how I see through my screen?

You're looking for some sort of remote control program. When I was an IT intern at a local dried fruit company, they used TeamViewer to remotely control all of the company computers. Although most of these programs are used to remotely control a PC, you can give the other person permission (or not) to control your PC. TeamViewer is free for personal use.

Yes, if that person is connected with your computer remotely using tools like R-HUB remote support servers, Teamviewer, Logmein etc. with your permission of course, he can completely control your computer. 

We use remote control software all the time for support. So the short answer is yes.

If you want something simple, for example, showing your mom how to do something on her computer, Skype has a "share screen" option, that will allow the persons in the same Skype call to see what you are doing. There are many others that are used for training, troubleshooting, presentations, etc.

There are other computer programs that can share your screen, mouse movements and even keystrokes with other people or allow them to take control of your computer remotely without your permission, so always be careful when installing stuff, especially if you get a call from Microsoft about a virus in your PC. Those are scams.

such software exists,yes. it is considered malware or spyware

Yes; it's called "remote desktop", or "remote access". There are a bunch of different products.

If you fall for a telephone scammer, he may try to install such software on your computer - so beware.