If the JT file is a BREP JT you can use the synchronous modeling commands to change delete ect. you can also add new feature to the prt. When you open the JT file with NX.
If you have access to the reverse engineering tools, then you can convert your JT file into a convergent body (use the 'Convert Facet Body' command). Once you have the convergent body, then you should be able to use it. Unfortunately for you you are still using NX 11. In NX 11, the set of tools available to modify convergent bodies is somewhat limited. In NX 12 and NX CR versions, there are many more things you can do to modify these bodies.
Having said that, once you do have a convergent body, you should be able to create section curves, define points, offset faces and many other things. So you should be able to do useful things with it.