The character meet and greets were ticketed and only on sea days on my recent eastern cruise. They have a morning session and an afternoon session. When you go to book the meet and greets online it will give you a time option.
The character breakfast is similar, but it is only offered once during the cruise in Animators. They play Disney Jr shows on the tv monitors. Your seating time is your seating time. They start by filling one side of the restaurant and work around filling in each and every table. The characters start with the people who have the earliest reservation time (thus the first ones seated) and work around the room meeting everyone one time (with breaks as necessary). Depending on your party size you can be seated with strangers. They have so many seats in the restaurant, and obviously only have enough reservations for those seats, so I don't think they like to leave many empty seats if possible.
Our characters were Sophia and Doc McStuffins (both whom I had never met before and both were adorable). We also had Goofy and Mickey. I don't think Jake is as prevalent anymore since he isn't being pushed as much on the Disney Junior channel. It's all Roadster Racer and Lion Guard still.