Just like checking at an Denny's. Show up, tell them you name and party number, if you want seating, and cell number, and they put you on the list. They'll give you an estimate as to when you might hear. I think they estimate ~2 hours per party, most don't stay that long.
When they text you they have space it means they have space right now. After ~15 minutes, they'll give it away. If you show up after they give it away (within a reasonable amount of time), they'll give you the option to wait and hang-out until space is available.
No, the terrace has a lot more space and less demand, I've never seen a wait. Terrace drinks are all "to go" drinks and come in plastic cups. You can still pay for the mug and pick it up at the Grog Grotto. Often, at night, there has been live music on the terrace. I did the GG once in our trip, but hung out on the terrace a few nights for a mai tai and live music.