Hey Deep!
Yes in the first few clips your absolutely right, your forehand goes into the net mainly because it’s just your arm doing the movement and there isn’t much help from the legs, body rotation and weight transfer going on. Yes also going for more spin will give you added safety, I think for you preparing for the shot early and making sure you have a very slight pause at the end of your backswing and then accelerating through the shot will help too, just to improve the timing and energy transfer. So try to imagine the shot is 2 parts with a pause in the middle,firstly the backswing and rotation,then the slight pause and the rotation forward,weight transfer and arm whipping through the ball, this will also help get the ball deeper like you mentioned.
Its good that you no longer have the problem of hitting into the net which shows you arw progressing well, I would just keeo going with this and really focus on the use of the legs and body more in the shot, especially before the contact. This will also allow you to keep your arm more relaxed and loose through the shot and use less effort so long term you’ll also be able to recover quicker too!
Keep up the good work Deep!
