1. You should start by taking your certificate code to Budget's site and popping it into the appropriate-looking field. Maybe it'll work...maybe it won't. If it doesn't work, you'll have to call Budget directly.

2. I've combined free-day certs before, but each one is different. You'll have to ask Budget and/or read the fine print on the cert you happen to have in your hand at the time.

3. Almost certainly NO it will not include a convertible.

4. Two possible hassles: it might be difficult to get the certificate rental properly set up as a FastBreak rental. That could subject you to a long line at the counter. Second, you could still get charged for significant taxes, fees, surcharges, etc. when using the certificate.

I know you aren't looking for a best-value-for-miles lecture, but in general, I've found that free car rental certificates never end up being worth what I was hoping for. I've used a couple in the past, and I've always had issues at pick-up or drop-off with getting the car I want or getting the total bill to come out right. It's a hassle, and usually only the manager can help you out.

I won't tell you how to use your AA miles, but I'll throw out other options: you could try Priceline to get your convertible at a reasonable cost. (Visit that travel-bidding site everybody talks about here to get an idea of what to bid.) Or Hotwire. Or just keep an eye out for good rental car deals in your FF statements and online.