It sounds like you want to export, then import web sessions. Select the sessions you want and Right-Click > Save > Selected Sessions > ArchiveZip
This creates a .saz file that you can then drag/drop in the session area (or File > Load Archive). Then, just right click the sessions you want and Replay > Reissue Requests.
If you want to "fiddle" with a request, you can drag/drop it into the Composer tab and change the headers/body.
To get more programmatic, you can File > Export > "Visual Studio Web Test" or you can use the Request To Code extension (I created it) to get code appropriate to reproduce the request and then put that in a program of your choice.