I have been in and out of Chef Mickey's in 50 minutes, and was seated early, but that is not the norm, to see all of the characters plan at least 90 minutes as pp suggested. At Chef Mickey's you check in, then wait, then they call you to take a picture, then you wait to be seated. Since this is in a hotel, remember to add travel time to the parks for any other reservations. Magic Kingdom is a 10 minute walk, or a 15-20 minute monorail ride, since the monorail will stop at Poly and Grand Floridian on the way to Magic Kingdom.
I have been in and out of BOG for lunch in 20 minutes, really it is as long as it takes to get seated and the food is almost instantaneous, if you pre-ordered. But I would suggest taking your time to soak in everything around you.
Akershus, is same as Chef Mickey's, check in then wait for your party to be called, take a picture with a princess and get seated. This is table side ordering so the meal is prepared fresh to order which takes a bit longer (appetizers are buffet style) and desserts. I would say there is no way to make illuminations FP and really you probably will miss the beginning of Illuminations if it starts at 9 PM. For the girls Akershus will be their FAVORITE!!! So many princesses, you really don't want to rush through this and miss even one princess. The princesses will engage with you, not just pose for pictures, sign an autograph and be off. Ariel even sat at our table and drew a picture with my 5 year old niece.
Good new about Illuminations though, right outside of Akershus hall and down by Germany there is some PRIME viewing areas no fast pass needed and never really crowded.
If you can move around some reservations to make the timing work, that would be best. Rushing through a meal to get to a FP is not very enjoyable. Believe me we have done it and our whole party was so frazzled by the time we made the FP reservation ( BOG Lunch to Seven Dwarfs Mine Train) we did not enjoy it as much as we should.
I have yet to try 1900 Fair Park, just keep in mind the travel time from the dinner to the park you want to go to.
Hollywood and Vine had the best desserts I had all trip, so set aside some room for those beauties. We went there for lunch to met Doc McStuffins and Princess Sofia and were in and out in 60 minutes. Dinner may be quicker because there are no characters.