What kind of animation? gif isn't suitable for anything elaborate. Simple animations like a blinking light or moving emoticons with only a few frames it works well for. For anything fancy you should use flash.
The other problem is there isn't much software available, when flash came along it pretty much put the nail in the coffin. There's only two that I'm aware of, Image ready that came with Photoshop and Ulead had a excellent .gif animator. I'm pretty sure neither is available anymore .
As far as the .ico do a search on google for favico.ico gnerator. There is lot of online tools that can do this. There's also png2ico but it's command line:
png2ico - PNG to icon converter (Linux,GNU,Windows,Unix)
Edit: FYI if you can find a older version of Photoimpact which should be pretty easy the full version came with a copy of the gif animator. I know up to until about version 9 or 10 that was the case but I can't gurantee anything.