You have essentially found what people are calling "the grind".
Once you have gotten you level 20 and ascention and switched class, you must purchase all your skills.
All skills are available, you just have to track down the Skill merchants. The skills you mentioned above can be found in ascalon.
Because you need skill points to get these new skills unlocked, you must level up your character many times. After 20 you are rewarded 1 skill point upon level up. So to unlock your next class completely, be prepared to level up your character another 25 times or so per class.
The other part is that everytime you purchase a skill. the price of your next skill goes up. Be prepared to see skills costing upwards of 1 plat each in the near future.
This is why many people find it more cost effective to simply unlock other classes with a brand new character.
I however disliked several missions so much i refused to repeat them and chose to do the grind.
This is what your xp will look like upon grinding through about 5 classes.