I think his editing his post
So will see it afterwards

Anyway, yeah, the way skills are appearing for you are more like they would in the manhwa 'The Gamer'
SAO skills earned from leveling abilities, I have no clue how they work, but you wouldn't be getting them so suddenly like that. There are a set of default ones skills and associated sub skills (sword skills) with each skill. As you level the skill more of those get unlocked, but skill leveling takes time. We have not made a system for skill leveling yet though.

Edit:
i am thinking level 5