A149:
1. You can use either the animals calculation or the Monks Unarmored Defense.
2. If you conduct an unarmed attack, you deal monk damage; if you opt to claw or bite, you do that damage.
3. Legal, though actually catching the missile may not be possible in some forms.
4. You can use Ki Wildshaped, and use Stunning Strike.
5. Bonus, you keep the monk movement speed too!
(All answers are for 5th ed; if the quandary was truly about 4th, please disregard 8).