can's meanings derived from capability

[keannu]

I think the meaning of 2,3,4,5 are all basically derived from 1. For example, in 3, "You can park your car here" means "I will give you such a capability to park here" and 2,4,5 all have the same "capability" nuance. What do you think?

1. I can in-line skate. - capability
2. Anybody can make a mistake - possibility
3 You can park your car here. - permission
4. Can she be truly happy? - strong doubt
5. He(Elvis Presley) is still alive? It cannot be possible - negative presumption.

[5jj]

I think it's stretching the meaning of 'capability'.