so what exactly is an amoeba?

Class Sarcodina
This class contains the amoebae (genus Amoeba), which move by sending out fingerlike projections called pseudopodia (meaning false feet) from the cell...
The cell body is a flexible mass of protoplasm except in the encysted stage. Because of this characteristic, amoebae lack a definate shape as this changes with the motion of the cellular contents.
-Volk & Wheeler: Basic Microbiology

Watching a living amoeba, you see one of the most flexible of all cells. Pseudopodia may bulge from virtually anywhere on the cell surface. When an amoeba moves, it extends a pseudopodium and anchors its tip, and then more cytoplasm streams into the pseudopodium. The cytoskeletom, consisting of microtubules and microfilaments, functions in amoeboid movement.
-Campbell: Biology

amoeba (a-me'ba), n.
a microscopic, one-celled animal found in stagnant water.
-amoebic adj.
The Pocket Webster School & Office Dictionary

An amoeba is more complex than a star and less predictable. An astronomer can, with reasonable confidence, predict just what a star will be doing one billion years from now, while a biologist can only guess what an amoeba will be doing 15 minutes from now.
-Isaac Asimov "life on earth"

Perhaps perfection is not possible in this universe. Or, if it is, perfection rules out progress. The amoeba is perfect, but it can't evolve into something different. Or, if it does, it ceases to be an amoeba, and must give up perfection for certain advantages, balanced or imbalanced with certain disadvantages.
-Philip Jose Farmer, Gods Of Riverworld

...God has been here all along, shaping us and being shaped by us in no particular way or in too many ways at once like an amoeba--or like a cancer. Chaos.
-Octavia Butler, Parable of the Sower

"Size isn't everything," said Ridcully. "People always smirk when they say that. I can't imagine why."
"You're absolutely right!" snapped the god, as if Ridcully had triggered an entirely new train of thought. "Look at amoebas, except that of course you can't because they're so small. Adaptable, efficient and practically immortal. Wonderful things, amoebas." His little eyes misted over. "Best day's work I ever did."
-Terry Pratchett, The Last Continent

The ameba has no feet.
-The World Book Encyclopedia