Can Aquamoeba beat Glory Seeker if the Aquamoeba owner discards one or more cards during the fight?
Discard a card from your hand: switch Aquamoeba's power and toughness until end of turn. 1/3 creature
2/2 creature - human soldier
It used to be the case that you could do this:
This would cause the Aquamoeba to have 3 power when damage was assigned but have 3 toughness when damage was resolved, killing the 2/2 but leaving the Aquamoeba alive.
However, changes to the combat rules for Magic 2010 were made that specifically prevented this. Now damage does not use the stack and is assigned and applied in one step, so the Aquamoeba can be either 1/3 at the time (and both survive) or 3/1 at the time (and both die).
Unless stated otherwise on the card, all activated abilities can be played at anytime, identical to an instant. This means you can activate Aquamoeba's ability during combat, and due to the way the Stack works Aquamoeba's ability will take effect before combat damage is dealt. Therefore using Aquamoeba's ability will result in both itself and Glory Seeker dying.
Yup it can. Card abilities can be activated like instants - therefore can be activated at any time of play. Although both creature would die because it does not have first strike.