Where to start. This is going to be a long post, I apologise.
45kg shoulder press and 60kg squat would be a ridiculous strength imbalance. It suggests that your technique is poor, to be honest.
One thing I immediately see is that you are not warming up nearly enough. This is almost certainly the reason your squat weight is so erratic. By the time you get to your work sets you should be warm, loose and ready to go. A couple of half-arsed sets with the bar or 40kg is not going to do this. Warm up sets are just as important as work sets, and are an opportunity for you to focus on your technique, so that you are ready to apply it to your work sets. Do lots of warm ups. Do not increase the weight until you are happy your technique with that weight is rock solid. That means you are getting low enough, you are tight enough, you're following the right cues, et cetera. If that means you do five sets with the bar, so be it. Warm up sets should not be easy. You should be squeezing every muscle, from your upper back to your hips and especially your core, as much as possible, just as you would on a max squat. They should be quick, they should be powerful. Even I, as someone who can squat about 2.5xbw, end up puffing after a set of 8 with the bar, because squeezing every muscle you use in the squat is difficult, even with a light weight.
Hell, even with no weight. Try it now. If your breathing isn't affected by a few deep, bw squats, you are being lazy.
The reason you're not getting low enough is because you're doing a sumo stance. There is no reason for you to do this. Feet should be a comfortable shoulder width, it'll make getting down a lot easier. Sumo can sometimes be useful for powerlifters who want to lift the maximum weight once, in a competition, to just parallel, but it is a crap way for a beginner to train for strength. There is a huge difference between moving as much weight as possible in the short term, and increasing strength in the long term. Stop it.
It is also one of the reasons you are bending over at the bottom. This isn't necessarily bad for your back, as long as you are bending at the hips rather than the spine, but as a beginner you probably want to bring your stance in and try to keep your chest up as much as possible. Everyone's going to bend slightly, but tbh 45 degrees is a lot, and if you're doing that at lighter weights it's not surprising you're being pushed down with heavier weights. I squat low-bar and yes, it means you're going to be further forward than with high bar, but you never want to focus on trying to bend down. That angle should be purely a by-product of pushing your hips back as you get into the hole.
The thing I would have you look at here is your upper back. It needs to be tight, and I mean uncomfortably tight. Bring your hands in until it is difficult to then get yourself under the bar, but not so much that it hurts your shoulders. Find that shelf in your rear delts, it may well not be as low as you think. Squeeze your upper back as much as possible and pull your elbows forwards and down. It will keep your chest up and back tight. Holding that position should be difficult. It should be something you have to focus on the whole lift. If you just grip onto the bar and forget about it, and you lose your upper back tightness, the weight will bend you over, both literally and metaphorically.
You also want to take a deep breath and really squeeze it inside you. This will keep your core tight and your back straight. You suggest that you are pulling your stomach in. You want to do exactly the opposite. Breath deeply into your belly as much as you possibly can, expanding your belly as much as possible, and then squeeze it hard. I hope this is what you meant by pulling your stomach in, because actually pulling your stomach in would be terrible.
Also stop doing leg presses. If you are squatting every workout you don't need them. They're crap anyway.
But yea, if you can't add 2.5kg to your squat every session at this stage you are doing something wrong, be it technique or just going to heavy too soon.