The effect from the ability overwrites other effects that set power and/or toughness if and only if those effects existed before the ability resolved. It will not overwrite effects that modify power or toughness (whether from a static ability, counters, or a resolved spell or ability), nor will it overwrite effects that set power and toughness which come into existence after the ability resolves. Effects that switch the creature's power and toughness are always applied after any other power or toughness changing effects, including this one, regardless of the order in which they are created.

If the second ability affects a creature, it doesn't cause that creature to lose any of its abilities. It just gives that creature flying as well.

The affected creature remains 3/1 and has flying as long as it has a feather counter on it. The effect continues even if Aven Mimeomancer leaves the battlefield.

You may put a feather counter on a creature that already has a feather counter on it. Doing so has no visible effect unless some other effect has changed the creature's power or toughness, or caused it to lose flying, since the last feather counter was put on it.

If all feather counters on a creature are moved to a different creature, the ability doesn't follow them. The first creature stops being affected by the ability because it no longer has a feather counter on it. The second creature is not affected by the ability because Aven Mimeomancer didn't target it.