On adding load...
Again, depends on the trainer. I have my own principles with it. Basically, when it comes to form, I think there's a little grey area between "safe" and "perfect". A movement can be safe but not perfect, in other words. An example would be a deadlift where the hips shoot up first, maybe even the UPPER back rounds a little, but the lower back remains in the it's neutral arch. Honestly, I don't see anything wrong with that, it's not perfect but, it's not dangerous. This is where I would NOT add load, this is where I would stop. In fact, I generally would stop before this point but this is as "bad" as it gets. Sometimes it's tough to call. I aim for perfect and taking it to a "perfect grind" - form doesn't change but the weight moves sloooowwwww. I'll try and stop here, any heavier and your form will change, in other words you will stray further from "perfect" and closer to "safe". You typically have a less-than-perfect-but-still-safe rep in you after the "perfect grind". Then, any heavier and it will just be a total mess. Going back to the deadlift, that's where you'll see lumbar flexion, and you really want to avoid that.
So, try and keep it perfect, but if you're trying to improve strength, try and take to a weight difficult enough that requires you to get your game-face on and grind through it. Sometimes you'll stray from perfect but it should still be safe if you're sensible. Obviously, i'm not talking about other methods such as speed work here.
With a squat, you can have the same issue, hips will move up first or faster, weight may fall forward, but your knees are tracking ok and your back is flat. No big deal, it'll happen if you're pushing it. However, don't let your knee cave in and don't let your back round - there's actually no reason other than ego to let this happen. Minor compensation occurs well before disaster. Stop at minor compensation -if you even get that far- and you'll avoid disaster. Strive to keep it perfect.
I get clients in to the mindset of fighting form vs fighting weight. Don't think about fighting 100KG, think about fighting to maintain form. The weight is just a tool to try and push you out of form, and your job is to fight it. If another rep, or another 10KG is going to push you out of form, then don't do it.
You want to strive for perfect form. On the big movements, think "one rep shy of failure" and also think "technical failure" vs "total failure". If you think the next rep "might" result in failure, just don't do it. Pick your battles wisely.
Strength training really is a marathon and not a sprint. If you turn it into a sprint you'll burn out and get injured. The best thing you can get out of a strength training session is a PB that leaves plates on the floor. For example you hit a 10KG PB on deadlift and feel like you have another 10KG in you. Leave it there. Be happy with the PB you got and bank that other 10KG you think you have. If you go for it you'll probably end up with an ugly rep at best. If you bank it, it's like an investment, the 10KG you left in the floor will be 20KG down the line.
Take this from someone who has regressed by ~20KG in squat and deadlift in the last 18 months.
Also (i'm just rambling all the things i say to clients about form here), reps build form, bad reps build bad form. An "ugly" rep doesn't help you one bit, it just strokes the ego. They're only allowed on test days or competitions which are effectively a "battle of egos" (nothing wrong with that, but accept the risk).
I can also say from experience that the more you practice perfect form the more you "cement" it (reps build form!). Have you ever noticed an advanced PL missing a deadlift, squat, or bench? Normally, his body doesn't change, form doesn't change, the bar just stops moving. Any deviation is very subtle. Then get a beginner or intermediate work up to failure - not recommended but you see it all the time. It's horrible, the body morphs into something completely different from the intended lift. Again, bad reps build bad form. Fight form, not weight, and honestly, the weight will go up, just be patient.
"Strength training is a skill" - Approaching technique like this is really the "skill" component of strength training. There's a lot going on when grinding out a big lift!
In that respect, I tell clients they need to EARN an increase in weight. If 100KG is safe but not perfect, they know they need to clean it up and own it before they get a shot at 110KG.
I've rambled on far too much but it's a topic close to my heart