Thévenin equivalent of a Norton equivalent
Yes and yes.  Man, that was an easy one!

Yes, you can convert between Thevenin and Norton equivalents just as you show here.  Even the math in the drawings is right, leading me to think you cut them out of a textbook but doubted their accuracy and wanted to double check.  (Good job, BTW...in engineering, doubt is always your friend.)

The two Thevenin equivalents are themselves equivalent because, as it's a 2-terminal black box with no connection to the intermediate node, the order doesn't matter.  You don't care what the voltage is at the intermediate node.  In the Norton equivalent, there are only two nodes, both of which are exposed, so there's fewer alternatives...unless you want to count the poorly but somewhat accurately analogous one of drawing the current source to the right and the resistor to the left.