That's alot of questions there Harish. Starting with what I believe to be the case about IP addresses ...unless anyone knows different. One thing could lead to another here.
If you are on dial-up, an IP address is individual to you for the as long as your current Internet session lasts. As SG says, when you log off from the Net the IP number you were using will be given to someone else. You'll get a different one next time you log on. IP addresses like this are said to be
Dynamically assigned.
The IP address
can remain the same if you have a permanent connection such as broadband provides. This isn't guaranteed by my ISP though. To get a guaranteed permanent IP address, so that I have a fixed Internet address, would cost extra I believe.
The purpose of an IP address is not to keep an eye on you, or to enable anyone to track you down. It is to let the sites you visit send information to your computer. If they didn't know your IP address you might ask a site to show you its pages but it wouldn't be able to do so. The reason being that it wouldn't know where to send the requested information to. Your IP address is like a return address. No IP address = no Internet communication.
Many people are concerned about their IP address being known because they think it leads straight to their computer and subsequently, to any information it has on it, such as street address, hair colour and favourite puddings etc. Not true. The IP address leads only as far as a person's ISP. As far as I'm aware, the only way to find out who a person is beyond that is with a Court Order instructing an ISP to disclose information.
In the case of a dial-up connection, this must be pretty difficult because the IP address is constantly changing. Perhaps it could be tied down to a group of people though, I'm not sure about that. It must be easier in the case of a permanently connected user where IP addresses don't change that much.
IP addresses can be used to breach computer security by nasty people who like to do such things. Once the IP address is known it can be scanned for what are called 'open ports'. Ports are used to connect your computer to various places on the Internet.
The remedy to this is simple. Get a firewall operational NOW. This closes any open ports on your computer. The nasty people then won't even know you're there!
In short;
The IP address enables the two way communication needed to take part in the Internet experience. Sites need to know it in order to show you stuff. That's how the Internet works.
No one can come knocking at your door, or learn your bank account details (or hair colour, favourite puddings etc), from just knowing your IP address. That would need the cooperation of the ISP.
Your IP address being known, in conjuction with
not having a firewall installed, makes your computer vulnerable to a security breach.
I said one thing could lead to another