Tox protects your privacy by:
Removing the need to rely on central authorities to provide messenger services
Concealing your identity (in the form of meta-data, e.g. your IP address) from people who are not your authorized friends
Enforcing end-to-end encryption with perfect forward secrecy as the default and only mode of operation for all messages
Making your identity impossible to forge without the possesion of your personal private key, which never leaves your computer
You can add people by giving them your ToxID, it usually looks like:
56A1ADE4B65B86BCD51CC73E2CD4E542179F47959FE3E0E21B4B0ACDADE51855D34D34D37CB5
In most clients you can find it in the Profile or Settings panel. Give yours to your friend and get your friend to add it. That's it.
If you want a shorter and more memorable ID, you can use a service like our ToxID server or an other ToxID instance, such as ToxMe. A ToxID maps an email-address-style username to a Tox ID. However, an individual concerned about their security should avoid using these services where possible.
Unfortunately, the cost of this convenient name-to-Tox ID mapping is a loss of decentralization. You must trust that the entity running the service is serving you (and others looking for you) accurate information. If you're not careful, you may be subject to MITM attacks.
Removing a contact means you can't interact with it.
If you remove someone from your contacts list, they will see you go offline, as if you closed your client normally. They can't communicate with you any longer until you add them to your contacts list again.
Not really. Strangers won't be able to get it. Your friends may get it. It's P2P
Tox makes no attempt to cloak your IP address when communicating with friends, as the whole point of a peer-to-peer network is to connect you directly to your friends. A workaround does exist in the form of tunneling your Tox connections through Tor. However, a non-friend user cannot discover your IP address using only a Tox ID; your IP address will only be discernible when you accept/send a friend request, and add a user to your contacts list.
See Also: What is stopping people from tracking me through the public DHT (advanced).