Shimano Bottom Bracket LHS cup - splines all worn off. Removal tips? In reference to one of these BB's: 

http://www.amazon.com/Shimano-UN54-Bottom-Bracket/dp/B0039369B4

My kid had successfully chamferred the left BB cup's  splines, until there is no useable spline surfaces left.  metal alloy, not plastic.
What happened was the Right cup worked it's way loose (by design!) and he just kept riding it until the left crank abraded the left cup to nothingness, that, and he couldn't pedal it any more ;).

Q1. What is the recommended extraction method for the mucked up left cup?   Dremel and cold chisel?
Q2. Does the LBS sell just the left cup?
Q3. To prevent a repeat, is it advisable to put some Lock Tite on the Right cup?  From what I can tell, the BB was never faced properly, and the RHS cup will continue to work loose, given it is a LH thread and is on the RHS.  

Thanks.
Jordan
Q1 - Removing the damaged left cup: I think I'd do this by first removing the crank arms and the right hand cup. Then, I'd remove the axle. Once you have it all apart you can work on removing the left hand cup. Since it has a right hand thread what I think I'd do is to get an screw extractor (aka an EasyOut). You can find sets online fairly inexpensively, Harbor Freight also carries them, and your local hardware or plumbing supply store will also have them. If you're going someplace local, take the right hand cup to make sure you get the right size. With the EasyOut you'll be able to back the cup out using the hole for the axle.

Q2 - Can you buy just the left cup: I'd be surprised if you could, but bottom brackets are relatively inexpensive. A descent conventional bottom bracket lists for US $30 and you can find them pretty easily discounted to about half of that. It seems likely that enough parts of that bottom bracket are damaged that it would be worth replacing the whole thing.

Q3 - Should you use a thread locking compound: You could, but it's probably unnecessary. The left hand thread is self-tightening as long as the bearings are doing their job. It's a bit counterintuitive at first, but think about how the bottom bracket works. From the right hand side the crank is turning clockwise. This causes the ball bearings to turn counter clockwise, so the motion of the bearings on the outside – against the bottom bracket cup – is working on tightening the left hand thread.