After Effects for Website application

I think for something like this, you'll be looking to recreate any projects outside of AE.  Is this for preview purposes or final product?

Services like VideoBolt already do this so it comes down to your interests and skill level I think.  If you're not into web  app coding, then it would probably be possible but it might be simpler to present 3-4 versions of each logo animation.  That way your customers can see what's possible.

That's entirely up to your web design skills and how you are able to translate your web code to AE native functions using scripts and plug-ins. That and of course you would need to even have a license for AE server-side use to even be able to provide such a service.

Mylenium