Passenger front wheel locking up when the A/C is on

That is very interesting! I've worked as a Ford dealer tech for 27 years and have never heard of anything like this. But what I can tell you is that the compressor clutch does often time induce noise into the system when it is bad, even though the clutch operates. The abs module should have generated a code if there was an issue with the internal valves but stranger things have happened. You can also take and put a voltmeter between the battery ground terminal and the chassis while the a/c is on to verify that there is less than 1 volt. If over 1 volt check the grounds or add an additional ground between the negative terminal and the chassis and also between the engine and the chassis just for insurance.

Attached is a video. When pressing the pedal to the floor there is a little popping noise when reaching the floor. Every time the noise happens the car will not move when in gear for a couple of seconds.

Sounds like something is mechanically touching the shaft when it is depressed. The booster, pedal bracket possibly.

After that sound Is made the pedal feels like there's no fluid until I bring it all the way up and it has pressure again. Of course this only happens in the driveway.

Either a mechanical issue with the master cylinder or booster would be my guess.

I can see it being the booster. The pedal does stick when it makes that clicking noise. However, can a booster problem like this make just one side lock up?

No it shouldn't, but what you can do is have someone press the brake pedal while releasing the left and right front bleeders to see how the fluid comes out, also during the lock up event.

Okay. And if the flow isn't strong usually it's recommended to change the caliper, but the caliper is new on that side.

I would just like to rule out anything on the master cylinder side of things.

So if the flow isn't good and the caliper is new, would you replace the master, or the ABS module?

At that point I would verify flow between the master cylinder and the ABS HCU (hydraulic control unit), if that is good then your concern will be with the ABS HCU, some are replaceable by themselves and others come with the module, ask your parts person for information on that part.

And you would verify that by loosening the line going to the HCU or from the HCU to the line for that wheel?

I would replace the brake flex line to the caliper to rule any kind of blockage out. Also lets do a CAN scan to see what comes up. Here is a video:

https://youtu.be/InIlnsjOVFA

Does the AC work okay?

AC works great. As far as the CAN, I have a Zurich ZR13 reader that can read ABS, SRS. EVAP, and power-train codes. That should suffice right? I did get a code under ABS, it was regarding battery voltage - a body code. I believe that was because the customer's car had died due to bad battery connection and was cleared after the terminals were fixed. Now there are no codes in the system.

Your scanner should do the trick! As far as the battery voltage code is concerned, if the battery went dead then the code you received is normal for that condition. As Ken noted, brake lines at the caliper are a failure point that should be taken into consideration, if it were my vehicle I would replace them! But that's just me. Also yes, you can crack the line at the hcu-to-caliper line or at the wheel to verify pressure.