I can think of one (very obvious) explanation: the squats have (possibly) just gotten progressively higher, creating the illusion that he is getting stronger.
OP, would you care to post a video of these squats? If you are 5’4" and 164 pounds and can squat 405 or more without any dedicated focus on squatting, you should consider powerlifting.
As for your other questions, the answer is “it depends” to just about all of them.
How much protein? 1 g/lb of bodyweight is a good general guideline.
How many days/week cardio? Hugely variable here. Some would recommend doing very little cardio and just reining in your diet. robstein gave you a good answer: start with just a little and then add as needed.
Should you try a different split? That’s been the subject of a few hundred threads in this forum, and will be the subject of a few hundred more, no doubt. Many of us who post here frequently seem to believe that the specific split matters less than the effort put into it.