You won't hurt anything running the engine with the plane held still. The only time it might be an issue is if you had an arragement that required forward motion to provide cooling air. Other than pushers, I don't think I've seen this.

You can run it around with out the wing if you want, no problem. You should cover the opening in the fuse with something to keep the oil and gunk out though.

Do be careful whenever you run an engine somewhere like your driveway. It's amazing how good the prop is at finding gravel and other small bits of junk and flinging it directly at your eyes. Most organized flying sites have had all the small bits of crud already flung out of the way by all the engines that have been run before you got there (ok, that's not exactly right, but you get the idea)