1. If I were to take the test in a left-hand drive car, would that limit the qualifications of my license somehow, similar to how if you pass the test driving a car with automatic transmission, your license would only qualify you to drive that type of car?
Nope, not at all. However the car would make the examiner much more nervous and probably leave you less likely to pass the test - and the pass rate right now is less than 50%
2. For the practical test, do you have the option of using one of their cars, and if so, roughly how much would that cost?
As was said before you can use your instructors car. It's always best to take a few lessons, no matter how long you have been driving. The charge is usually the same as for 2 hours of driving lessons
3. My mother, a U.S. citizen, lives in France but doesn't have a prayer of passing the French driver's test seeing as it took her more than 3 years to learn how to say "Hi, how are you?" in French. She can't exchange her U.S. license directly for a French one, thus she'd like to get a UK license and then exchange it for a French one. How hard would it be for her to tell a bit of a white lie and say she currently lives at my address, in order to take the UK test? How thorough is the DVLA in trying to verify that you are indeed a UK resident? The other thing is, she'd have to ensure that getting a UK license that's for an automatic car could be exchanged for a French one...need to verify that.
No idea. What the DVLA says is If you want to take a GB driving test you must be normally resident in Great Britain. However, if you have moved to GB having recently been permanently resident in another state of the EC/EEA, you must have been normally resident in GB for 185 days in the 12 months prior to your application for a driving test and a full licence I have no idea how well they verify that.
Rosie