You have absolutely no core engagement when squat, that's why you can't support yourself when you get low. That is why your back arches immediately when you start your squat, if your abs were tight you wouldn't have nearly as much lumbar nor thoracic movement. It also explains why you fall over when you get to the bottom, in the short spot where you drop down at the end, you do a complete but wink. Your muscles are not contracting and you have no base, hence why you are wobbly and fall.
A few pointers. Find someone in real life who will help you. Surely there is someone who is knowledgeable in squatting who can help.
Next up, do not start the squat but shooting your hips back, this will cause you to arch your back, as you start reaching backwards with your hips instead of pulling yourself down. Instead start with pulling your knees outwards, that way at least you will be starting the movement with your glutes and creating enough space for you to lower your hips down.
Next thing is learn how to engage your core, at the bottom of your squat you should be bracing your abs like you are defending yourself from a punch and pulling up on your pelvic floor.
You can practice by holding onto something and sitting down into a squat and completely relaxed, you should be able to sit there just fine. if your heels come up then open up your stance. spread your feet and knees, but not too much. sit at the bottom and get comfortable. Then squeeze your glutes and abs (remember bracing for a punch) this should automatically lift you up a few inches. This will be the bottom of your squat for now. This is the lowest point from where you can control your core while you squat.
practice holding that spot, if it is above your knees so be it, but I guarantee that it will be lower and with better form than where you are squatting now. Once you can hold it, practice squatting up to 85% lockout and back down, taking 3 to 5 seconds in each direction really feeling out what is going on.
From there hold onto a weight, i.e. goblet squat, and keep on goblet squatting until 15 reps with a with a weight that you can barely hold onto. From there you will be mostly ready to back squat properly.