No, it is rignt now working instead of the NLA and not together with the NLA. When you start the addon then it will also remove the old NLA tracks.
After working with animation layers you can always turn it off and continue working with the NLA
It is planned in the future to make it work better together, without removing your NLA tracks when starting (or at least it will be optional)

No, but it's a great idea. I'm considering it as a feature request for the future.
Right now you can load an action quickly into a layer by selecting the layer and then selecting the action in the action editor

The addon is working per object. So you probably just need to select an object or armature if you want the animation layers tab to appear