I don't consider 6C as cold because you don't know where HA is.
What is that 3H bid? just forcing or showing HA? The 4H bid is okay only if 3H shows HA. Maybe misunderstanding here.
The minimum for opening 2C is not met by North. If DK is HA instead, that would be minimum for opening 2C.
You were thinking 7 when bidding 5S? From what I see, 5S is cue bid, not for strength in S. It can't be passed. If you bid 4S after 4H, that's showing strength.