Will my cousin be a perfect match for me for organ donation?

No: It's unlikely that cousins will be "perfect matches" but it's also unnecessary. Most donors only need to have compatible blood types in order to get a good result since today's medicines are so effective.

Not necessarily: It would depend on the tissue type of both the donor and the recipient and the degree of sensitization of the recipient (prior transplants, blood transfusions, pregnancies if any, viral infections, etc.). The proper testing needs to be done.