Anonymous SMS

1) It works by faking/changing the sender info through direct access to an operator's SMSC.

2) An operator can trace it. Whether it is legal or not depends on what country you are in (what laws apply), and what you use it for. Consult a lawyer in your country (or in every country you're interested in).

3) They're there in the plain at the SMSC, unless you write your own client-side application that encrypts the message content before sending it (the receiver must then also have a corresponding client application to decrypt the message, and you also need to figure out how to distribute encryption/decryption keys separately, securely). Of course, network operator's system administrators are probably in most countries not legally allowed to monitor SMS content for other people, but if they wish to do so by breaking laws and employment contracts, they can, if they have the appropriate access to the SMSC.

4) It depends on the SMSC implementation. Talk to SMSC system vendors to know how their systems operate and how they can be configured (and to know how a particular operator has configured their SMSC and how they use it, you have to ask them). Not also that local and international laws might apply here, too.

5) There is no such as "free SMS" (whomever does the actual SMS sending will always be billed by the network operator somehow), but there can be free services for consumers, and a "free SMS" service provider connecs to an operator's SMSC and they get their money through some other means (or stop offering the service when they cannot any longer pay their bills to the network operator for delivering the SMS).