If an elven unit is fighting an enemy unit where only one character has ASF, and all elves are attacking the unit not the character, how is ASF resolved?

Does the character effectively prevent rerolls on his unit?

No.

What matters is the whether the models you are attacking have ASF (or high initiative). Other models in the combat don't matter for that purpose.

If both sides have ASF then the model with this duke it out first. If the lone character has a higher initiative than the elves he is first in combat, potentially killing off some pointy eared snobs before they attack. Then all attacks from the elves go against the unit and the unit, or what's left of it strikes back.

That's at least my limited understanding and reasoning of the situation without lawyer reading the BRB and the legolas codex.

As Dyvim said, if your say witch elves duke it out with, say, empire greatswords and an empire hero with the ASF sword. And your WE strike the greatswords. It goes like this: WE has ASF, their close combat target does not and their I is at or lower than yours --> you get rerolls.

If your WE instead direct attacks on the hero, they do not get any rerolls.

The close combat phase proceeds like this, cirka.

Impact hits and related are resolved before anything else.

Then, all models with ASF strike simultaneously, regardless of initiative on either side. First is first, no matter what. However, models with ASF dont get rerolls attacking other models with ASF, also regardless of initiative on either side. This also means if 3 elf heroes are in combat, and the attacks of the first two remove number 3 from base contact with enemies, the third guy still gets to swing because it all happens simultaneously.

Then, other attacks are resolved in initiative order.

Finally, attacks with ASL (such as empire greatswords) are resolved, along with stomps and thunderstomps if any.