Yes, starting with Firetask 3.1, you can sync your Firetask repository with our desktop version Firetask for Mac.
Yes, Firetask 3.0 is optimized for iOS 4 and includes a complete set of high-resolution images. It supports multitasking/fast app switching and looks even better than ever before on the iPhone 4's new retina display.
Your task will only appear on today when it really becomes relevant to you. A task becomes relevant when it is either due today or within the next five days, if it is the first actionable task for you in a project, or if the task in question is marked as flagged.
The "Waiting for" category is a concept we borrowed from David Allen's "Getting Things Done® - GTD®" way of managing tasks. Basically, you use this category to keep track of tasks you are not doing yourself, but delegating to other people.
The "In-Tray" is a concept for storing your thoughts and ideas, things you do not yet know what to do about. As soon as you have decided what to do with them you can, e.g., make them "Actionable" or you delay them to "Someday" - simply by changing their status.
Yes, you can backup your data to our desktop version Firetask for Mac via syncing.