fly, cut, surf, waterfall, rock smash, strength, and rock climb (don't get till you beat all 16 gyms, from prof oak)
You can't get rid of HMs in heartgold.
In the top of the battle tower
double click on them then click toss
train your pokemon up to level 80,90, or 100 and teach it TMs and HMs
rock smash water fall strengh surf and flash
The only way to delete moves is through the Move Deleter, which should be in Blackthorn City.
The code is: 1356475a 89065865 00000000 00000078 90765937 98765000
there usally in town or around town but when ur at the island with the fighting type Pokemon gym you have to beat the gym first and if u go north swicune should be there
same as the old ones if you've played the old version remember it a nicer lookin remake with more stuff to do that's it
There is no best Pokemon on Pokemon HeartGold.
there is no Pokemon Mansion in Heartgold.
Surf East from New Bark Town, then there you are. If you wish to progress to Route 26 then you will need Pokemon that know the Surf and Waterfall HMs and the gym badges that allow you to use them out of battle.