There's a door. In a way like the art piece along the wall forward from Tuscan that looks like an inside view of the hull---except it's actually the hall wall for the deck 3 starboard cabins.
And as such the lower price. Don't worry about it. Like @mom says, bag tags aren't necessary. Your cabin assignment could pop up on the app at any time---check there.
Although they didn't, one would feel FBC has an inherent obligation to take the lead in coordinating with the airline to connect the bags with the ship.
Your concern is noted, but all reputable shore excursions group will operate their tours (one I'm familiar with starts at 4:30, lasts about 4 hours) in conjunction with ships in port. Plus, their tour begins/ends practically adjacent to the tender. Also, there will be lots of passengers coming down after viewing the sunset from Fira.
If you want to share---ask. They'll accommodate if possible. And in spite of many "the sky is falling" concerns about the change to all anytime dining, there have yet to be many reports of substantive waits to be seated in the MDRs.