Wow that was difficult to read.

Let me see if I can answer everything:
1. What is Google Voice:
Google Voice is a service provided by Google to provide what is essentially a "trunking" service. In the old days (very old), to make a phone call, you had to pick up the phone, talk to a human operator and tell that person to connect you to your actual destination. The operator would then initiate a call to the other party, and then connect that line to your line.
Nowadays, the human operator is replaced by a computerized switchboard at your telco that essentially does the same thing.
Google Voice (GV) does pretty much the same thing too.
You tell GV that you want to dial your friend "A". GV then calls you at one of your registered phone numbers. Once you pick up, GV then calls your friend A, and connects you two together.
What are these "registered numbers"?
Those are your actual phone numbers. It may be a real phone (tmobile/att/whatever) or it could be a VOIP solution like SIP or Skype - as long as it has a number that GV can call.

2. Do I have to pay to call people?
It depends: GV does not charge you (yet) for the 2 phone calls it makes - one to you and one to your friend A.
However, the fact that GV makes a phone call to your number means that your phone is being charged some air time from your telco. If you have a plan that has incoming free (like a home phone), then for all intents and purposes, the call is free for you.
If it is a regular cellphone plan, then you pay the airtime minutes that your telco charges.
Most SIP accounts have free incoming, and so if you configure GV to call your SIP number, then all you're paying for is your Internet expenses.
If you're using SIP on a data plan, then you're paying because of data plan charges.
In summary: It depends on your configuration.

3. Can I call only gvoice numbers? Only to computers no cellphone?:
GV calls your friend A's phone number. It is a phone trunking service. There isn't as yet any concept of differentiating between normal phone numbers and the number GV gives you.

4. You're the latest to ask these questions. I am sure there are many others who still struggle to understand GV and why it is useful.