Maybe it's unpopular, but I think people should avoid dangerous lifts like the deadlift and the barbell back squat. There's so much that can go wrong with those exercises that, I think the cost benefit is too low.
Cardio is a necessity and not an enemy. By doing 20-30 minutes of high intensity cardio, above 150 bpms, you'll be training your body to use fat as energy fuel and to better use Oxygen. Better use of oxygen also means faster muscle recovery.
I thought diets were binary. Bulk mode or Cut mode. This is wrong, they should be done in a gradual way. Otherwise, they can lead to a lot of fat gain in the beginning of a Bulk and a lot of muscle loss in the beginning of a Cut. Instead, add or decrease 200 calories until your weight doesn't change anymore.
You are reaching the limits of what your muscles can accomplish. The only way to increase this limit, is to gain muscle mass. Also, if you're doing push ups, try to do pull ups to balance your physique. Push ups train mostly chest and triceps, if you only focus on that you'll create muscle imbalances in your body in the long term. A strong chest with a weak back will lead to poor posture, which in IT is quite a common problem.