You're welcome.
You'll come on leaps and bounds if you lower your squat weight and go for 15 reps for example (if you usually do 6-10 reps) and get that core and lower back stronger.
All sorts of things work your core. Do standing barbell curls with super strict form and slowly then you'll feel your core has been worked. You just can't do a curl without engaging your abs/core. If they weren't working you'd just double over forwards if you weren't using your core to keep you upright.
Lower back, do bent over rows at about 25 degrees or 3 of clock (if you imagine your body is the hour hand and your legs the minutes, your body will be pointing to 3 or 4 on the clock. You probably know that but I just wanted to explain thoroughly)
Weighted sit ups, hanging leg raises with ankle weights. All good. And the big one, Deadlifts. But they can really bum your back if you're out of form with them.