The 6th gym (Steel type) does not unlock any new HM , instead the 16th Gym (Blue's Gym) unlocks Rock Climb
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After you beat Blue, the 16th gym leader
Head back to new bark town and use surf on the water.
All you have to do is beat gym leaders then the allow you to use HM's out of battle but ether before or after battling the gym leader. Good Luck!
you use strength. you get strength on route 42. you can use it in the wild after you beat the goldenrod city gym.
After you beat Sabrina, the 6th gym leader in Saffron City, you can use Rock Smash.