Back Brakes Occasionally Lock Up - unsure of cause and how to fix

Over last month or so, I have had 3 brake problems that may be related.

1. ONE MONTH AGO- One day, while driving, I heard/felt a slight pop sound as if I ran over something small. Upon coming to stop light, I smelled strong burn smell and saw smoke from back of car. It was the back left brake. I pulled over, examined brake, and it appears the back left brake had locked up for some reason. Thinking back to the “pop” I had heard and felt, I guessed that the Emergency/Parking brake had not properly disengaged and the “pop” might have been it releasing. For several weeks, I did not have a problem and thought it was a random event.

2. SUNDAY MORNING- I was in NY state and the temperature was near zero. Upon starting the car that morning, when I began backing up, something felt off. It seemed I needed to give the car more gas than needed. I was unsure, due to driving on snow. After driving a short distance, I heard a very loud noise from back right brake. The back right wheel was entirely locked up and was being dragged upon the ice. I stopped the car, then tried going again. Upon moving an inch or two, there was a loud THUD, and the wheel would lock again. On the dash, the “ABS” light would came on. I turned the car off and started it again. The ABS light went off. Upon driving a couple inches, the THUD and ABS light came on again. However, upon putting the car in reverse, I could drive backwards just fine with no serious resistance from the brake problem. But upon driving forward, the problem came back. I did notice that as I attempted to pull and release the Emergency/parking brake, there seemed to be no resistance at all, causing me to think the emergency brake may not have properly disengaged (as supposed in the first brake problem). I do not know if this could somehow result in triggering the ABS causing the wheel to lock or not. I also am not sure if the severe cold may have contributed to this. There did not appear to be ice build up on the wheels or brake area. After parking the car in a garage over Sunday night, the problem seemed to disappear by Monday morning.

3. YESTERDAY- Monday, the car drove just fine with no evidence of brake problems. Tuesday, upon coming to a stop light, I smelled a moderately strong burning smell. Unsure if it was my vehicle, I did not stop. Upon getting to my destination, I examined each wheel. The back left brake had a strong burning smell, much like the 1st problem one month ago. The back left brake was the only one to have this smell. My best assumption is that the brake may have locked up, possibly related to the Emergency brake not disengaging.

Summary:
1st Problem- Felt a pop, saw smoke and strong burn smell from back left brake. Problem disappeared.
2nd Problem- Seems E-brake was locked. ABS completely locked back right wheel. Problem resolved next day in slightly warmer environment.
3rd Problem- Strong burn smell coming from back left brake. Problem resolved itself.

My Best Guess:
Problem with E-brake not properly disengaging. I do not know how this could be connected with the ABS completely locking the back right brake.

Update- Local Tire Shop Explanation:
Upon taking it to the tire shop for an oil change, I explained problem. They said they would take a look at it. Afterwards, they recommended replacing the back calipers, back brake pads, back rotors, and flushing the brake system. I asked for explanation. He said that the brake fluid was likely corrupted from moisture and that because it is corrosive, it ruined the calipers- causing them to lock up. He said that caused the brake pads to overheat and ruin. And that this caused the rotors to get warped. He said the brake fluid likely boiled and went up through the brake lines- requiring a flush. All of this sounds possible, but I was slightly suspicious for the following reasons- 1. When the brakes are not acting up, they seem to be working great. 2. There is absolutely no vibration while braking, which I would expect if rotors are warped. 3. The condition of the brake pads can not really be determined without disassembling the caliper. 4. This still does not explain the lack of tension on the E-brake in problem #2. 5. Nor does it seem to explain the triggering of the ABS system, which is what seized the back right wheel on problem #2. I am not opposed to getting all of this fixed, but I really would like a second opinion before I waste a bunch of money redoing the entire back brake system. Only to find out the problem was not resolved.