Congratulations on your new fence. To answer your questions, you have to refer to your contract.
1. A picture will tell us more how they did the gates.
2. Did you write it down in the contract? "Asking" is not the same.
3. A picture will help.
4. We know nothing about the boards you chose - what kind and what grade. However, split, cracked, bowed boards would be unacceptable.
You are so lucky not to have made the final payment. Have the company fulfill their part of the deal, item by item (including providing you a material lien release) before you pay them off. Holding the final payment is your only leverage. Keep in mind that holding the final payment after all corrections are made to both sides' satisfaction, is unlawful.