How do RC airplanes create thrust without using propellers or rockets?
They create thrust the same way that the full size ones do. 


In the case of a piston engine type aircraft they have either have a miniature version of a piston engine, or an electric motor which turns the propeller.
In the case of jet engine, like your picture, they have miniature versions of a jet engine.
Sometimes, the jet engine in an RC aircraft is actually a propeller made to look like a jet engine.



  Also, how do they control aileron


Usually by using servos to pull cables and pullies - essentially like aircraft used to before fly-by-wire systems were introduced.


  Does an RC plane have rudder?


Some do, some don't. Its the difference between 2 and 3 axis controls. Anything like the one in your picture almost certainly do.


  Do RCs have to be registered with local aviation authorities


Sometimes, It depends on jurisdiction and and often weight.