Question: Why was Elizabeth crying at home when she read the news article?
Answer: She is crying because Simon is back in her life. And she knows that the only reason for that would be that her hypnosis worked. She reads the article and she knows what he has done, even though he isn't aware of it. As we see later in the movie he was not really a nice guy, especially not to her.
Question: Just who all are all those other Sawyers in the opening scene? I saw The Cook and Grandpa but who were the rest and why were they there?
Answer: We are to presume they are extended family members and/or associates of the family that we simply didn't see in the original film.
Question: The method of identifying citizens by a "tattoo" burned into their arm seems awfully prehistoric for such an advanced environment. The government would "know" the number of legit citizens and would know that the black market citizens were fake, right?
Chosen answer: There is virtually no system in the world that is completely foolproof when it comes to regulating a large scale system related to identification. We only know the tattoo are for certain services. There might be more high tech security features for more restricted areas. As for whether they have an accurate count of all their citizens, they might, but again, how you go about regulating these systems is generally the tougher part. At the end of the day people required special transports to even reach Elysium, so it might have not been as big a concern.
Question: As the rain comes and the creatures come out and start to damage the station and kill people, why did the entire crew not seek refuge in their ships? Obviously, if the ships were meant for the harshness of space travel and some offensive/defensive capabilities, wouldn't they most likely have provided enough protection from the organic weapons of the creatures? It would make the plot not work but maybe should have been eliminated as a possibility.
Answer: The walls of the settlement are likely to be just as strong as the hulls of the spacecraft. It's likely they are even stronger because the settlement doesn't have to worry about weight limits. Remember also that they had to worry about Riddick hiding and getting the units back.
Chosen answer: The significance of showing the blood drop on Gerry's tongue and him spitting it out was to back up the theory that the only way to become a zombie is to be bitten by one. After the blood touched his tongue he ran to the edge of the building and waited 12 seconds (the time it takes to become a zombie) before he stepped off the ledge. If he would have started to change he was going to attempt to jump off the roof before causing harm to his family.
Then how does the scientist at the WHO get infected from a blood sample?
You can't turn by ingesting, or getting the blood on you. It has to enter your bloodstream. The scientist cut his hand and got zombie blood into his bloodstream.
He stuck himself with an infected needle or a "sharps" tool coated with infected fluids, which cut him.
Blood tester is encased in glass. Dr. Testing did not pay attention. His hand was in the case while it was mixing. Glass broke, cut him, testing blood mixed with his.