Yes to both :-) Umieć means to know how to, in the sense of having a skill, being able or capable to do something. There are no specific word in English meaning the same as umieć, so it would be translated using different verbs in different contexts.
- "Umiem liczyć"-> I know how to count.
- "Umiem latać" -> I can fly.
- "Umiem pływać" -> I can swim.
As those are verbs of motion, they actually care about the Present Simple/Present Continuous distinction.
"lecieć" - happens 'right now' or denotes a plan, therefore it translates to Present Continuous. "latać" - happens 'in general', so it translates to Present Simple. It can also mean "to be flying" if you are flying 'right now' but without destination nor direction, just flying around.
As here it's about the general ability to fly, it needs "latać".
Fruwać is a lot less common, but still acceptable, added now.
The -acz ending creates a noun which refers to someone or something that performs the action of the corresponding verb. So fruwacz would denote someone/something whose most characteristic property is the ability to fly. But it's a hypothetical word which isn't really in use.