Does an enemy with "immune to player cards" mean that Merry's stats are all zeros when attacking or defending against such enemy?

No.

Merry's card text:: Merry gets +1 [Attack] for each Hobbit hero you control.

This ability is only really affecting Merry, not the enemies they attack, so it works fine.
The ability applies, he gets the indicated amount of attack and attack is part of the game's basic framework so it works just fine in combat, pretty much regardless of where it came from.

As a contrast, consider Bard's ability, which lowers the enemies defense by 2, that does not work on immune enemies since it is trying to affect them, not just Bard.