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1. What is your take on the matter?
You don't sound like you want to be set up with that girl at all. Why are you even considering it, then? Because she's desperate for someone and your cousin wants you to?
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2. How should I approach my cousin about the situation?
"Hey cousin, I'm not looking to date anyone right now. It was nice of you to think of me, though. Thanks, anyway."
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3. Should I share my feelings with that person (the one I can not forget)?
She turned you down, yes? Then you basically told her your feelings already. Telling her again is probably not going to change her mind.
Edit: Also,
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I am not ugly I give myself a 9 out of 10.
A 9? Really?