Not impossible. The issue is if you roll in at 1pm, you may struggle to find one. But in the morning hours, I've had good luck finding them. They may not be dead center, but chairs open up here and there.
Absolutely not. MDR food is great, enjoy it!
The very back and front of the ship on the pool decks is last to get filled up. Also, indoor pool area (not the Solarium, the general public indoor pool) often has more seating.
I enjoyed it quite a bit. They have a great selection and it's a bit different variety of food than in the Windjammer.
Yes you can, but timing that activity can be tough. You'd best call Adventure Ocean and inquire about what time it will occur.
Voila: https://www.royalcaribbeanblog.com/2017/04/05/top-10-royal-caribbean-anthem-of-the-seas-hidden-secrets