Would appreciate clarification on the following:
Can you move diagonally?
Yes but... you must follow the rule of thumb which says you can cross any space that is not wider than the base of your figure. So there are some diagonals - especially in the courtyard - that are too wide and you must move around orthogonality.
Is a minion that is next to a mouse diagonally also adjacent?
If their base reaches - yes. But this does bring up a good question of a mouse vs. large minion where adjacency might not be recipricol.
If you can move diagonally can you cross spaces where the corners do not touch due to a small rock / artwork space being in between?
Yes, this is covered in the rules.
What about artwork on spaces, are these objects you have to go round?
Again, covered in the rules. If it is in a space, count it as part of the space. If it looks like it would block things, the group decides how to handle it.