Question: I am wondering whether its possible to change/set/delete my session variable AS A USER.

I am re-thinking the way that I do login realm in PHP. The way that I do it now is that I check whether a certain session variable is set or not. However, this would break if someone can just change his/her session variable.

Answer: 
Given that you do not have a method / form (inadvertently or actively) to allow the user to actively change this data, no. They should not be able to change their username etc. 

Since session data is stored on the server, yea, they would be hard set to set this themselves. If register\_globals is turned on, this might be a possibility, but that would also require other circumstances to be true. 

But in the whole, no, a user should not be able to change the session data unless you provide them a means to.
No, you have complete control over the session content.

All the user can do is remove the session cookie, thus dissociating himself from a given session, but he cannot change its contents.