It does! You will see the Simple FCurves panel in the Dope Sheet editor too.

Yes and no, depending on what you want to do. Simple FCurves lets you achieve the most common shapes used in animation straight from the timeline. The addon also lets you fine tune the curvatures in a way that's usually enough. Some specific cases though might require you to tweak the handles manually in the Graph Editor.

Yes you can! For most cases anyways. The only case where you are restricted to one curve at a time is the "Edit noise" function. You can however apply noise to several curves at once.

No, you don't have to hold your left mouse button. The first click on any of the designed buttons will enable the drag mode: the more you drag it to the right, the more extreme the changes will be. A second LMB click will apply the changes.

As of version 1.03 you totally can! The only case where you are restricted to one object are the functions related to adding, removing and editing noise.