Glad it’s going well! Any positive physique changes?
You could progress the dips either way, nothing wrong with upping the rep ranges and aiming for sets of 20. Adding weight is fine too as long as you don’t sacrifice form. Another option is slowing down the lowering phase to like an 8 sec negative, or adding a pause in the bottom position. Depends what you prefer and what you feel would benefit you more. Personally I would up the rep range/ slow down the lowering phase and get sets of 20 before adding weight.
Pressing from the bottom is fine for your goals. Yes you could get an extra rep or so starting from the top but your muscles only know tension and fatigue, they can’t count reps! Yes if you was working in lower rep ranges and couldn’t press the desired weight from the bottom it may hinder progress but I think you will be fine with what you are doing.