The quarterback hands the ball to a receiver; the handoff is in front of the quarterback but behind the line of scrimmage, which is a legal play.
Can the receiver now throw a forward pass?
Like already explained in my other answer, the Hand-Off is not a pass, so yes... a pass may still be thrown as long as the passing rules are met (only one forward pass per play, ball didn't cross the line before, etc).
Handing the ball is transferring player possession from one teammate to another without passing or kicking it. (Rules Section 15)
There is no statement in the rules of (in)eligible pass throwers, so anyone may do so.
Also Julian Edelman (Wide Receiver) threw a TD pass in 2015: Ravens vs Patriots
No, it'd be illegal. If the hand off is forward, it counts as a forward pass. If the receiver of that forward hand off then throws a forward pass it'd be considered the second forward pass of the play and thus be illegal.