None of these are paradoxes (paradi?).
Archimedes Paradox is simply a mistatement of the principle. If the density of the object is less then the fluid, then a smaller volume of fluid will be displaced. There is no circumstance that leads to no fluid will be displaced.
The wheel paradox is created by ignoring what is actually taking place. The line left on any surface is a projection of each circle from the POV of the axis/midpoint of the circles. The further away the surface is from that midpoint, the longer the projection. If the distance to the surface is the same as the radius of any circle, the projected length is the same as the circumference of that circle. Any circle with radius less than the distance to the surface, the projection will be larger than the circumference. For any circle with radius greater than the distance, the projection will be less than the circumference.
Fermi's (seeming) Paradox is just that, an apparent paradox--or just Fermi's Puzzle. It indicates that either our premises are faulty and/or our data is incomplete. This applies also to any "paradox" involving time travel or any other hypothetical situation.
The Lottery is just a misunderstanding (or deliberate misstatement) of probability.
Most paradoxes are just linguistic twists. Reality operates on a fixed set of rules. Language is arbitrary and inconsistent. Need I say more?
Genuine paradoxes do not exist in reality. The advancement of science relies on that. Consider, for example, Curie's discovery of radium. She knew, before even starting out, that there was something there we knew nothing about.