Two red children in a red-black tree
If 2 and 3 are both true, then the red-black trees you are sudying are not the standard ones, i.e., the ones from wikipedia.

The red nodes are usually assumed to be "satellites" of the black node above. If there is at most one red node attached to a black one that means either one or to keays belong together (with altogether either two or three pointers to their children). That nicely corresponds to a 2-3 tree.

The "usual" red-black trees can have two red children (but no red child to a red node) and correspond to 2-4 trees.