Is it possible for a young kid to know he or she is gay?

Possibly. Questions like this are most easily answered by asking the same question, replacing the word "gay" with the word "straight." at some point in development, children develop an attraction toward others in a pre-sexual way and just as a child may know that the preference is towards the opposite sex, a preference for the same sex can be just as certain. It is best to avoid judgements towards children.
Depends. Many teens start to have feelings of attraction to people of the opposite or same gender in early adolescence (age 13 to 15 years). Some youth discover feeling of attraction a bit earlier. Same sex attractions do not necessarily mean someone is gay or lesbian, but can be a sign of an emerging sexual orientation.