Damage from a source with infect has no effect on Melira's Keepers. No -1/-1 counters are placed on it, and no damage is marked on it. The damage is still dealt for purposes of effects that care about damage, such as lifelink.

If a creature with a counter on it becomes a copy of Melira's Keepers, those counters will remain.

If Melira's Keepers would enter with a counter on it, it simply enters without that counter.

Melira's Keepers can't have any kind of counters placed on it, not just -1/-1 counters.