HoMM3 HD is a mod (add-on) for the game Heroes of Might and Magic 3.

Why can't all 4 nodes in the center be connected by roads?

They can't be, roads rarely form a closed loop, only in the case of some kind of bug.

It is also possible to have roads along 2 opposite sides or not along any sides at all (is that so?)

It's not possible, there is only one road network, and it can only split in the case of a complex bug.