Why does Red Queen become an Omnicidal Maniac, when this was specifically stated by the first film to be the exact opposite of her goal?
If she was the same Red Queen from the first movie, perhaps she was driven insane by her 'death' and subsequent re-activation and holds a grudge against humanity for 'killing' her.
Alternately, she might've always been plotting to eliminate humanity, and just claimed to have been trying to avert the T-virus's escape as an excuse so the strike team wouldn't fry her immediately. She knew Umbrella would re-open the Hive, re-activate her, and inevitably set the virus loose with their reckless experimentation; she just needed to remain active long enough to ensure the antidote didn't make it to the surface and pass into the hands of an Umbrella-competitor she couldn't manipulate.
Also possible is that she may be seeking to kill all humanity so that no new monsters can be created and then when all the monsters rot away, the virus will be destroyed. It could be seen as burning the forest around a town when a large forest fire is approaching. When the fire reaches the area that has already been burned, it is forced to go out because there is no new fuel. Maybe she is applying the same theory to the virus.
Maybe the simple answer is that the Red Queen is merely a copy of the same A.I. program, with different objectives, or that the original was reprogrammed.
Wasn't the planet mostly a desert??
No. The same film that claimed that the T-Virus was destroying water, also contradicted it by having the final scenes take place in an exuberant rainstorm.
It's possible that the cure the White Queen was talking about in Extinction was partially successful in that it restored life to the planet, but didn't destroy the virus, or something.
Why does Alice know sign language? The Becky's Mom clone would know because of Becky. The initial signs could be seen as simple gestures if you don't know American Sign Language, but it becomes obvious later that she possess a competent knowledge of the language.
She could have learned it at any point in her life before the first movie. Its not really far fetched at all.
Pre-first-movie Alice was a trained Umbrella security agent/spy. It's possible that sign language is one of the skills such agents are taught, so they can covertly talk to each other in rooms that are bugged for audio.
Confirmed by a deleted scene in Becky's house.
Here's one. How long was Alice unconscious for at the start of the movie? It makes it seem like Alice and the others save the survivors, Umbrella attacks, Alice has a dream, and then Alice gets new clothes. It seems like she was out for a few hours to a day at most. However, if you think about it, she must have been out far longer. Especially, if Wesker was able to get so at home in the White House. So maybe a week but then how did she survive when it looks like they just strip searched her and threw her in a room until she woke up?
Another thing to consider is from the novelization where Red Queen is not responsible for the attack on humanity and instead Umbrella is still a corporation ran by humans who are trying to learn how to control the virus and failing. If we assume Alice was out for a day at most, that means Wesker was working for Umbrella, nearly died but escaped, and then somehow convinced the good guys to accept him and trust him enough to send a small group of trained men to rescue Alice all in a few hours. Either the good guys are really grasping at straws or Alice was out for far longer than it seems. Although this does bring up another question. Why would anyone trust Wesker in under a month considering how he was kidnapping innocent people until seconds before the start of Retribution?
They like his sunglasses. Alternatively it's been a fair while since Afterlife happened and Alice has just been kept unconcious for the whole time. Also only four people alive would know that Wesker used to be the head of Umbrella, and three of them are unaccounted for. When some form of superman shows up and starts helping in your desperate fight for survival, most people aren't going to look a gift horse in the mouth.