The plant wouldn't have flash frozen. Flash freezing means that most of the heat energy of the object is transmitted to the surrounding environment. This depends on having a lot of colder particles surrounding the object, so that there can be very many interactions that leave the particles of the object at a reduced energy state. But there aren't any colder particles in a vacuum. Space is a good insulator; whatever heat you have, you keep, because there's nowhere for it to go.
Instead, its surface water would have boiled:
"At NASA's Manned Spacecraft Center (now renamed Johnson Space Center) we had a test subject accidentally exposed to a near vacuum (less than 1 psi) in an incident involving a leaking space suit in a vacuum chamber back in '65. He remained concious for about 14 seconds, which is about the time it takes for O2 deprived blood to go from the lungs to the brain. The suit probably did not reach a hard vacuum, and we began repressurizing the chamber within 15 seconds. The subject regained conciousness at around 15,000 feet equivalent altitude. The subject later reported that he could feel and hear the air leaking out, and his last conscious memory was of the water on his tongue beginning to boil."
To answer your other questions:
1. When we first see the spaceship, I think we see debris and junk in orbit near it. Presumably the waste from the spaceship is being ejected into space.
2. Because the robots on the spaceship are indoor robots, not earth class robots. (That's what the -E on Wall-E means.) Wall-E seems quite a bit smarter than the ship-bound robots; perhaps increased intelligence is necessary to deal with the unpredictable Earth environment. Also, maybe there were larger robots in the Earth clean-up effort, but they broke down sooner because they require more power.
3. Robot operated mining camps on Mars.
4. If there aren't any thin people, we'll fuck fat people. We'll fuck a toaster if we have to. (It will have to be very brave.) And our cities only have trees because there are any trees. If there weren't any, we wouldn't have any, right? Also, if the autopilot or the news system has total control of all information dissemination to the passengers, how would they know that thin people or trees ever existed? Remember, Old-Earth newsreels were a revelation to the captain.
5. At the beginning we see that the Earth has a brown atmosphere. I think we're meant to believe that atmospheric poisoning has indeed occurred.
6. Take all the oxygen out and everything dies. See: Gulf of Mexico dead zone.
7. How do you know what he thinks? Maybe the first time he had to cannibalize another Wall-E unit, he was heartbroken about it. Maybe it took him a hundred years to work up the nerve. Maybe he's inured to it through simple repetition. Or maybe he only developed emotions last week. Also, he's a robot.
8. Because they left a lot of really smart, heavily armed autonomous robots behind on Earth, and robots are known to go crazy (hence the sanitarium on the ship). Also, how do you know Eve robots weren't previously used to put down the rebellion among the Venusian swamp monsters?
9. Because each individual robot or computer subassembly is individually sentient, or at least has its own personality and opinions. What you call the "main computer" is the autopilot, a powerful but not necessarily all-powerful entity aboard ship. Or even if the autopilot is all-powerful (except for the off switch), it may be following a cargo cult version of the instructions left by the founders, which may have included sending out the Eve robots - the auto-pilot might not even know what they're for.
10. Perhaps Wall-E, being himself a robot who has transcended and altered his programming, understood that Eve would eventually be capable of doing the same--but in the meantime would follow her directives. Perhaps his decision to undertake significant risk in order to allow her personality to flower could be seen as heroic. Also, have you ever been to a singles bar? If cute girls had lasers in their heads, this is exactly what it would be like.
11. How do you know that maintenance robots weren't replacing the defective display panels right up until last week? For that matter, why do you assume any of this stuff is electronic? Maybe those display panels are some advanced form of e-ink, or some further technology we haven't invented yet.
12. Wall-E feeds the cockroach. That's why it's still alive. We even see him doing it. That's also why abandoning the cockroach to take the rocket ride was such a big deal.
Did you even watch the movie? :-)