Assignments are so random that not sure what anyone else got will matter much for you. Assume you can get assigned any cabin on the ship but more likely one of the categories which still shows availability.
More like a couple of weeks before - very little is populated four months out or even two months out. But, for ships which don't change much while at the same home port, like O class, you can assume info even several months out will be very similar to current info.
Yes, using one of your D+ vouchers.
Sometimes, when the DL coffee machine is out of service, they might provide a daily coffee allowance on top of the regular D+ drink vouchers.
If you set the app to the next sailing (7/7) of Radiance (not yours), which should be southbound, it should list the formal nights (click on the Welcome Aboard portion and scroll through the days toward the bottom it should list the recommended dress - may be labeled as "dress to impress" instead of "formal").
The info for your sailing may not be complete in the app - that's why you should look at the current sailing. The info in the app gets better and more accurate/complete as you approach your sailing sate.
The OP's tour starts with a ferry ride (from the tender landing spot), so no issue with the cable car going up - it's only the end of the tour cable car down that will be the issue. They are also on a ship tour, so they'll likely be on a dedicated likely early tender.
There are two types of groups. The one the TA mentioned you establish yourself at the current pricing and you get a discount once your reach 8 cabins.
The second type of group is the kind the TA establishes. That has refundable rates, can be combined with discounts and many times is at a price lower than the published NRD rates.
It's this latter type you are looking for - available mainly at the bigger TAs.