You're making the points that:
- Queen vs Pawn on 7th rank of a-, c-, f-, or h-files is usually drawn.
- Queen vs Pawn on 7th rank of b-, d-, e-, or g-files is usually won.
- Queen vs 2 Pawns is usually won.
If one's seeking to deepen their understanding, they might also explore:
- When is Q vs P on 7th rank on a-, c-, f-, or h-files won? The easy answer is when the attacker's king is nearby. But to really master this endgame one has to know how near is near enough, and that takes study.
- What happens (even on the 6th rank) when the queen has no good checks.
Then one can test their understanding with interesting positions. For example, in the below White can gain two tempi and then he's near enough to win.
This shows when the Queen and King can stop the pawn from promoting.