Spellcasting

For the Spellcasting trait, you use the listed spellcaster level as read on page 10 of the Monster Manual:

The spellcaster level is also used for any cantrips included in the feature.

This means an archmage is treated as level 18 for the purposes of cantrips, and Nezznar is treated as level 4 (despite his greater number of hit dice).

Innate Spellcasting

Innate Spellcasting will sometimes list a specific level (in which case use that one), but otherwise you use the monster's CR (as also stated on page 10 of the Monster Manual):

If a monster has a cantrip where its level matters and no level is given, use the monster's challenge rating.

For the green hag, this means it is treated as level 3 for its cantrips.

I would rule that the original and the duplicates all have the effect of faerie fire visible. Faerie fire would outline all the duplicates and give advantage on attack rolls regardless. However while the spell does say

A duplicate can be destroyed only by an attack that hits it. It ignores all other damage and effects.

Mirror Image also says

Until the spell ends, the duplicates move with you and mimic your actions, shifting position so it's impossible to track which image is real.

I think that the duplicates would not be affected by faerie fire directly BUT seeing as the original is affected, they would alter their appearance to match that of the original thus conferring advantage to attacks made on them as the advantage is a result of faerie fire's outline making it easy to see the affected creature. (Otherwise why would the spell have to specify "if the attacker can see it"?)