"Here's SOME kiwi fruit for you" if it is an indefinite amount. "Here's A kiwi fruit for you" if it is a single one. People often leave off the word 'fruit' and just say 'kiwi'.

"Here's some kiwi fruit for you." is what I say and hear all the time.

The first sentence is correct.

I think thet first option is correct

This is debatable, because some people may consider "fruit" a countable noun or uncountable noun (fruit vs. fruits) They both can be correct in theory ( fruit and vegetables or fruits and vegetables )