I really need an API for side bar.

I'd like to remove it. I hate animation in this cases.

Spellchecking - yes, shortcut - no.

It can be done in plugin, but this is not for plugins ideas - -1.
You need to think about what needs this plugins. I mean API for sidebar - this is good idea.

Better if we'll get this functionality in the context menu of the folders.

Better to show it in the title. For example: "ST2 - Proj1 (UNREGISTERED)".

Oh, it's not really needs. If you are using it or different machines, make a configs for each other, like in other editors or IDEs.

It needs to be pretty smart, but, in the common codding, it needs in very small cases. Anyway, Joe have more priority problems. You can try to make this idea after general things will be done.

It's already grabs colors from GTK theme. See some shots at http://blog.soulrobber.ru/2011/01/30/sublime-text-2/
For the side panel, it's much harder, because need to make sexy gradient and effects. Better to change it in theme. In this case - see upper, we already have an idea:
http://sublimetext.userecho.com/feedback/19274-theming-of-the-sidebar/

We really need this for working with most of code projects.