In Code: Veronica X, Wesker knows Steve's name. But Steve's dead, they never met before then, and there's no indication whatsoever that Wesker heard a few of the conversations in-game that would indicate that his name was Steve.
Steve was a prisoner of an Umbrella-run facility, and they would keep track of that sort of thing. Wesker had access to the facility's files by virtue of having just taken it over by force.
To quote The Dark Id regarding Claire's imprisonment on the island: "Instead of turning her over to the police like rational people, we decided to kidnap her and ship her off to our corporate branch death camp." Umbrella routinely makes stupid decisions, but there is seriously no real reason for them to lock up Claire themselves. It would be understandable if she knew corporate secrets or something, but she broke into the Paris lab facility specifically because she was looking for answers and any claims she made to the police would probably be dismissed.
Not necessarily. According to RE4's intro movie, after the thing in Raccoon City, the US Government started seriously looking at Umbrella and shut them down. Code Veronica would've been happening just as that investigation was getting started, so she would not have been so quickly dismissed.
Considering that Claire is one of the few survivors of the Raccoon City outbreak, and probably had some of those files picked up in the labs in RE2 ready to testify against Umbrella, it may not be as stupid as it seems. Then again, Wesker could have just decided to keep Claire around to lure Chris in.
Except that he had already betrayed Umbrella by that point. He wouldn't have been the one who made the decision to ship her off to Rockfort — the one responsible for that decision would have had to have been either Ozwell Spencer, Alfred Ashford, or whoever ran that facility she had broken into. I think the third is most likely, though he may have had to get Spencer's and/or Alfred's approval first — we don't have any way of knowing about that.
Where are those giant tentacles coming from? Are the coming from Alexia directly? Are they under the base? Why are there a bunch of giant tentacles under the base?
Why are there zombies in the Antarctic base before Alexia is revived?