dbk747,
1. No. Brakes are not covered under the factory warranty after 12 months or 12 miles, and only then if it is not a "Normal wear" issue.
2. I get my remanufactured calipers at the local autopart stores, like AutoZone, O'Reilly's, Pep Boys, NAPA, etc. Check around and compare prices and warranties. You will need to return your old calipers (there is a core charge) so make sure you get them back from your mechanic and return them ASAP to get your core charge refunded. I do not recommend paying more money to get a LifeTime warranty, since I always do a brake job just before the 50K mile caliper warranty is up. Since I always get between 45K and 50K miles on a set of front brake pads, that works out to about 2-3 brake jobs over the life of the vehicle (150K-200K miles)
3. Any brand of brake fluid should be fine for a street driven vehicle as long as it meets or exceeds the DOT specs for your vehicle. If you are going to have your brake fluid flushed, bring plenty. Your mechanic will need close to a quart of fluid. You can keep the rest to top off your master cylinder if the level drops as the brakes wear. However, brake fluid is hydroscopic (absorbs water from the atmosphere) and has a limited shelf life after it is opened. If it's over a year old, I would throw it away. You don't want to put that contaminated fluid into your brake system, it will lead to corrosion forming in your brakes, especially in the calipers since they are the lowest points in the braking system, and that leads to calipers sticking, which is probably your problem now.
Lastly, make sure your mechanic lubes the caliper slide pins and the brake pad tabs that slide on the caliper frame. There is a special grease designed for use on brake components to help keep the moving parts from sticking but does not melt and run all over everything when it gets hot...and it will get very hot.
...Rich