Interpreting a geological map
1. What is the youngest/oldest rock in the geological history of this map.

Your approach is the right one but isn't the limestone  underlain by something? Drawing the AB cross section would be of great help here, did you manage to do that?

2. What type of fold is shown on the map.

What is the definition of a syncline and does your interpretation agree with your answer to question one?
Are there any legend symbols on the map which would be used to indicate a fold?

3. Brief geological history of map

Putting all the lithologies and the deformation (Question 2) in right order would be a big part of that. After that maybe you have some ideas about a succession of claystone, limestone and mudstone