The Axion used some kind of FTL drive to return to Earth but the probe ship used subluminal speeds to return to the Axion from Earth. A speed that would have taken years, if not centuries, for the trip shown.

Using chemical reactive propulsion to land a giant ship and then take off again is a horribly inefficient way to get six Eve's down to the surface of earth. Especially when repeated to retrieve them. Especially when the technology for artificial gravity and anti-gravity apparently exists and is used widely (Eve flies without any apparent form of propulsion).

It is essentially impossible to evacuate earth. The planet's population increases by about 250,000 every day. Based on the size of the Axiom as seen when it lands on Earth, just to hold the population of Earth steady would require at least one new Axion be build every day and probably dozens if you want to evacuate the planet in any short period of time.

If the planet was evacuated, where are all of the other cruise ships out in space and will they be returning?

If the planet wasn't evacuated, where are the signs of 6+ billion corpses among all the trash?

Either that is the universes smallest nebula that the Axion is living behind or the Axion was much bigger in space than it was on Earth.

I'm pretty sure that 700 years far exceeds the data life of VHS (and in reality a VHS tape would be decades older than the Earth evacuation). An, really, the artifacts he was finding were amazingly well preserved for being 700+ years old in an area ravaged by severe storms.

Why is a short term probe designed to look for plantlife on an otherwise sterile planet so heavily armed and aggressively programmed? What is Eve designed to defend herself from?

It was pretty, but of course the rings of Saturn are not so dense that you can run a hand through them.

Why did the Axion have a complement of plant-seeking probes when they apparently departed on their 5-year cruise expecting it to be just 5 years and with earth still occupied by a clean up force consisting of at least Fred Willard?

Earth deprived of plant life for 700 years would be extremely oxygen deprived. The existence of a single photosynthesizing plant would hardly indicate that the atmosphere had returned to a survivable balance.

If there had been no plants on the planet for 700 years where did the plant found germinate from?

Presumably there are plenty of other cockroaches or is the one we meet 700 years old? If so, what are they eating since no new food is being created?

Since Wall-E is solar powered and the trip from Earth to the Axion must have taken days or weeks (even if not shown but obviously not the years or centuries of reality) and most of the would have been in the essentially zero-light of extra-solar space travel how was he still charged when reaching the Axion?