Hi,
The stabilization feature is one of the more process intensive editing functions, so it can sometimes take a while to complete, particularly of you have a large clip or a clip with considerable shaking. It shouldn't take forever, though. Possibly the delay is caused by a corrupt preference that is affecting the functionality.
Try restarting your computer and opening iMovie while holding down the Option and Command keys and selecting to delete preferences in the box that appears. iMovie will open in a new library. Reopen your old library to get back to your projects. Now see if the stabilization feature works.
iMovie sets the project frame rate and resolution as that of the first clip placed in a newly created project. So, if for example you want a 30fps frame rate for the project you set that by placing a known 30fps clip into the project as the first clip added to a newly created project. That will set it at 30fps. You can delete the clip later if you want without it affecting the frame rate that has been set.
-- Rich