No, the real-world is neither a matrix nor is neo a super-hero who can do anything. His powers in the real world come only from the fact that his contact with the Source conected him to the Machine mainframe so he can do things like stop sentinels but not fly or use the powers he has in the matrix. Here is a statement I posted earlier in a different thread:
If Neo's powers were just telekenesis or to "move or stop objects," then they would be too limited. We have been told that he can "alter the matrix as he [sees] fit." We have to interpret this as that as long as he understands fully that the matrix isn't real that the only real limit to his powers is his mind (which he has demonstrated is pretty free). In otherwords his powers are potentially unlimited.
As for the means of his powers, when he plugs into the matrix, it's like he's feeding it his mind data. It cannot reject his mind. In this way he is sort of one with the matrix, and because it cannot alter his mind(This is his fundamental power as The One, otherwise he would be no different from other freed humans in the matrix) it must succomb to his will when there is a confliction. This means that his powers lie in the extent of his belief. For example: if it is written in the matrix that the daggers(in the Merovingian's) are at rest, but Neo believes that they are flying towards his hands, since the matrix can't force him to believe that they are still on the wall, it must accept that the daggers are, as Neo believes, in fact flying towards him. This then becomes what the matrix sees as truth and consequently tells all those plugged into it. Naturally, forcing yourself to believe something is not easy which is what makes Neo unique.
As for the programs in the matrix: Because they aren't rules of the matrix, nor are they a part of the matrix itself, Neo is not directly connected to them. This is why he cannot simply make the agents disapear(or do something to that effect); however, all of the programs in the matrix are still subject to the matrix's rules(as well as what the matrix has made to be truth) which is how Neo, who can alter the matrix itself, can still have a measure of controll over virtually all programs in the matrix.
Probably the reason that he hasn't become some sort of "Uberneo" is because he has only, of yet, discovered a limited extent of his powers and I think that in the third film we can expect to see that as he becomes more and more in controll of his powers there will be more absolutely ridiculously amazing things that he does.
Let me remind you that everything I have just stated are simply my own conclusions which I have drawn from the films(as well as the video game and Animatrix) and I by no means beliave that I am neccessarily correct in everything. I just think people should draw what they can from this.
Thanks for reading this.