Regarding tank removal: If possible, I would strongly recommend having an assistant the first time. If not possible, you can still do it, but that first time is tricky.
1.) Take off the seat and remove the two bolts that hold down the seat bracket and the rear of the gas tank.
2.) Remove the speedometer cable where it screws on to the transmission. This is on the right side of the bike. It looks like a great long spring running from the tranny up under the tank. Just unscrew it and pull it of BEING VERY CAREFUL NOT TO LOSE THE WASHER THAT IS INSIDE THE SCREW CAP. Put a baggie or piece of tape on the bottom of the cable to retain the washer.
3.) Remove the vacuum line and fuel line from the carburetor and let them hang from the petcock.
4.) Lift gently on the back of the tank while pushing slightly to the left side of the bike. This will allow you to get the petcock past the frame. Pull back and up. The tank is anchored in the front by to half-sockets that rest on rubber doughnuts mounted to the frame. The primary motion you are looking for is backward, but a little lift and left will be necessary.
5.) You will know when the tank is loose. When it is, turn it partially onto its side, and unhook the wires that lead to the speedo. There is a white plug close to the tank. Just pull it apart. There is also a rubber hose on mine that hooks to the tank toward the front on the right. Pluck that off as well.
6.) There you have it. Set the tank somewhere safe.
If I missed anything, someone will jump in. Good luck...
Regarding the vibration: If you can describe it a little better, and tell us what you and the bike are doing when it happens, there will be no end of suggestions forthcoming. I promise.