If a player uses Forced March on a Hero, and moves that Hero to another zone where there is already a Hero, can the two Hero coexist in the same zone?

"His opponent also cannot play, give
control of, move, or put into play (via
a card effect) another Hero into that
zone." (FAQ, p. 8)

In simple words. The game prevents you from doing that. You're never allowed to force a situation, such as two heroes in the same zone, that is forbidden by the rules.

but what about a unit that has the text "battlefield only"? He can only be played into the battlefield but can he be moved to another zone by a game effect such as forced march?

Yep. The "battlefield only" statements only apply to where he can be played. This statement does not limit where he can be moved.