Does this avoid the Maroczy Bind?

Logically, it would seem to force a response of Nc3.
However, there are several thousand games in the master database from this position. Not one took the pawn.

What if white begins with 3.c4 before d4?

Indeed there is nothing wrong to take that pawn, just pawn up for nothing.
I had a look on my database, only 6 or 7 games, (not really master level...), and no one played Nxe4. The reason seems quite obvious for me, it is just misprint or mistake when entering moves.
Of course 5.c4 doesnt make any sense unless u want to play with an handicap.