If you mean Chef Mickeys, then yes, it is a character breakfast buffet. I believe the last seating in at 11:30, and they do not serve lunch. We went for breakfast in June, and they had tons of options! Pretty much any kind of breakfast item you can think of, plus more! Im not really sure what clarifies as "Brunch" (there were no 'lunch' food items per say) but there was TONS of food to choose from! You wont be stuck with just a bagel. It was a great time. It is at the Contemporary Resort, we hopped onto the monorail from the Magic Kingdom. It was quick and easy to get to!
You will not have to pay for your 2.5 year old. He will be able to eat from the buffet for free. Anyone under the age of 3 years old is not required to pay at the buffet meals at Disney.
You asked if "all of the breakfasts were character meals". If you mean at Chef Mickeys, then, yes-- every day they have characters there to interact with you while you are dining.
If you meant, 'are all breakfasts buffets in Disney character meals', then no. But, There are a few other character breakfasts within the Disney parks, and resorts to choose from. Off the top of my head, I can think of The Cape May Cafe with Minnie, Goofy Chip, and Dale; Tusker House Breakfast with Donald and Friends; 1900 Park Fare with Mary Poppins, Alice, and Mad Hatter.
Happy to help! Enjoy your meals! I went in June with 2.5 year old twins, a 2 year old, and a 1 year old. Everyone but the 2 year old LOVED the characters and reallllly enjoyed dining with them at character meals! Plus, it saves time waiting in line at the parks to meet with a chracter. We would just say "We dont have to stand in line to meet Pluto now, we are having dinner with him tomorrow". It worked great!
Heres a picture with Donald at Chef Mickeys:
