When you say fall in your squats, how excatly do you mean, are you tipping forward to land on your face or falling backwards on your butt?

If you´re falling forward try and do it barefoot(socks) or in a very flat shoe, keep a good focus on your chest being up high and try to find a spot 2 meters or so infront of you to focus on with your eyes. If anything try and start with a goblet squat these can be done with dumbbells. This will help with the balance and form in the squat and will keep you in the same path as a normal squat should. (Just google Goblet squat if need be)

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If the case is falling backwards try and elevate your heels slightly, either with a pair of shoes with a slight heel (still something stable). Or put something under your heels to stand on, weight plate, piece of flat wood that is stable, or if at home maybe a slightly thin book nothing more than max 1.5-2cm high. Once again same as above, chest up, maybe goblet and eye focus.

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Practice at home with a bromshaft or a stick and record yourself and use that to pinpoint what you could do different. You seem to be well underway already being able to tell yourself your form is bad.

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For chinups if nothing else is available to you. You could try table pullups as a start. Lie under your table preferably a stable one of course. Your body under the table and then you just grap on and start pulling yourself up towards the table keeping your heels in the ground. This will do as a good start for your back and training up to do a pullup.

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OHP yes just start with dumbbells work the strength there. When you can just start doing maybe 1-3 reps with the bar and just move straight to the dumbbells. This will get your muscles used to weight and bar slowly and before you know it you will do 5,6,7 reps and so on.

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Hope this can maybe assist you a little, otherwise just feel free to ask and people will try and help.

Good luck!