Do Breaks Get Stuck?

No, but brakes do.

Yes they do . When your car or vehicle is siting too long they will seize up. It can be that your brake hose doesnt release the pressure like my van had that problem. I just had to buy a new brake hose . Good luck .

My experience is that brakes normally don't stick unless you have bad or dirty caliper pistons or maybe your driving with the emergency brake engaged. Sticky brakes are a result of heat build up, due to the piston not retracting back into the caliper. Hope this helps.

Yes,the caliper,the shoes ,the pads can all get stuck and drag on the drum or rotors .you should notice a metallic burning smell or be able to feel excessive heat by touching the rim/wheel of your vehicle after driving a short distance.i just replaced my brake pads and the guide pins that hold the caliper because of this.