I recently had my brakes worked on. The master cylinder and booster were replaced. The first day I noticed I either had to barely tap the pedal or it was going half way down. On the third day the brakes locked up, I couldn’t reverse or go forward for several minutes. I took the car back, the mechanic explained that they were on factory settings and that probably caused them to overheat. He said he loosened it and it was fine. It felt like it did before he worked on it. I took it back again. He said he drove it around and that they were working properly. I am still having to push the pedal to the floor. I don’t feel safe driving my car. What exactly could be the problem?
The phrase "they were on factory settings and that probably caused them them to overheat" sounds pretty dubious to me and makes me suspect that your mechanic may be up to something, perhaps trying to cover up a mistake, or it's possible you have been ripped off. There's no factory setting that would overheat your brakes and nothing to loosen. If your brakes had been fixed properly you would have none of these issues.
Some of the issues you describe sound like air in the brake lines, which is simple to fix with the right tools and should have been done as a routine part of replacing your master cylinder. Brakes not releasing wouldn't be air in the lines though, it could be a bad brake caliper or the master cylinder installed hasn't been done right.
A home mechanic with the right tools could look into this, the first thing I would do is look under the hood to see if they'd actually replaced anything. You should be able to tell if your master cylinder/booster assembly is new as it should be shiny. If you have no mechanic skills I would suggest you take this to a different mechanic for a second opinion, ask them to determine what work was done and what is wrong now. If you can't do that I would go straight to the manager of the shop the mechanic works at and demand they look into it, or if its a chain talk to their complaints department.
First of all, change your mechanic shop !!
Jack lift the car wheels one by one then try to rotate them manually. Check and take your readings. Note that which wheel is dragging more then the other.
Imagining, only two wheels require more force to spin manually. Now, reinstall the brake pads, lubricate the brake caliper pins on these two wheels only.
Overhauling the brake pistons and/or wheel cylinders accordingly is always recommended when replacing any brake parts. Your car service manual (available online) gives the oem recommended brake fluid bleeding sequence for all the four wheels to remove air from the brake lines/system.
Nonetheless, a little drag is always there, when using aftermarket spare parts for first few miles, after replacement.