I can't help with the the antenna problem since I haven't had to do anything to mine yet (137k miles so I'm probably not far behind you on it...lol) but the headlight problem is most likely with the small bushings that are in the gear assembly. For a nice page of pic's to see what's inside your light's, look
here. Credit for that page goes to someone else that posted a link a week or so ago, I just saved it cuz...well...it's a good page to bookmark! It's a reasonably simple job, although it'll probably be just a little time consuming your first time. Mine was just slightly different from the pictures on the page linked, in photo #5 where it shows where you've removed the bolt's/nuts from, the extra one all the way to the right isn't there on mine....it's the same one that in photo #3 is the nut on the bracket to the far right. Only thing I can figure is a difference in year models for whatever reason? (mine is a 92 coupe) You'll probably want to go ahead and do them on both sides, not just the one that's messing up, the other most likely isn't far behind it unless you know of it being changed already. Your gear is probably fine, just make sure to clean the teeth on it...and everything else...out from the remains of the dead bushings. They're cheap too, 5-7$ roughly depending on where you get them from and I think all the corvette parts supplier's will have them. If you search the forums you'll find more on this headlight problem.
Edit--One other thing, when I did mine last weekend, the small pin that you have to remove, I had to replace both of those, which are another very inexpensive small part so you may want to have those handy or be prepared for a trip to the parts store. Then again, I haven't heard of other people having them come out broken, so mine might have just been a freak thing.