The first is grammatical but not very natural. You could improve it by replacing "a" with "the", though it'd sound better reworded.
The second isn't correct. "Skiing" here is a singular noun (a gerund) and needs "activity", not "activities".
You don't need "kind of" here unless there's some specific reason for it. You could just say, "Apples are the fruit I eat every day"? Or, even simpler, "I eat apples every day". (I wasn't sure why you wanted to use "kind of" in your sentences on skiing either.)