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.
The user can't act on session variables, except through whatever functionality you expose. The session variables are stored on the server and are not exposed to the user automatically.

The only thing that the user may be able to do is mess with the session id.