So I'll give my opinion on Babcock leaving and everything first. I honestly sort of want him gone. We could use a change of pace and the veteran-run team is getting old. If he begins to use our youth adequately, I'll probably feel differently as he is an incredible coach. I also think he's comfortable in Detroit and is going to be here for a long time. He likes Holland, and he likes his team. I'd be very surprised if he moves on.
As far as why he hasn't signed yet, I'm not sure. Most of the articles and his statements I've seen suggest two possibilities. The first is just that it isn't a big deal. He doesn't need a contract right now, and he has no reason to sign one immediately. He might as well wait and see if the team tanks or something. The other strong possibility is that he gets a little bit more power because of the contract. He has the "Give me this roster or I walk" card to play. Now the third possibility is he wants out, but I haven't seen anything to suggest that. So we'll just have to wait.
As far as Shanny goes, they obviously know and have worked with one another, and I'd assume they like each other. But I honestly don't know. If Babcock does leave, I have no idea where he'd go. I guess Shanahan in Toronto is appealing, but I'm sure he can find a connection to almost any team, so for you guys I wouldn't say he's a slam dunk to go there.
That's my two cents. I didn't feel like finding sources, but I'm sure a google News search of "babcock" will give you everything you need.