Auto Trace. You need to expand the trace before you can edit it. With the trace selected, hit the Expand button in the tool options along the top. Auto tracing is certainly a useful feature in Illustrator, but the fact that you have to Expand it to edit it is not intuitive. Illustrator is not intuitive or user friendly, but a complex tool (no shit!).
Drawing freehand is certainly an option in Illustrator, however it's not the way that most people will use the software, it can be useful of those who need to draw sketches/line drawings and such like, but that's only a small part of what Illustrator can be used for. Freehand drawing/painting might be what you are familiar with when using raster software, but it's not the way Illustrator really works at it's core. A wacom tablet is useful for drawing freehand, but not for much else in Illustrator (in my personal opinion). I find a mouse to be more useful generally, much more so than in Photoshop for example.
Altering strokes you drew freehand with the Pencil/Brush tool: that behaviour can be changed in the the tool options. Double click the Pencil or Brush tool icon to bring up the options, where you can change the amount of smoothing.
Erasing in Illustrator is an entirely different concept from that used in raster software. When you use the eraser, it cuts/eats into a shape (a closed path) and changes the path and anchors, and for open paths it removes part of a path, and it's anchors, and adds new anchors. In certain circumstances it can alter the appearance of a stroke in unexpected ways, e.g. if you have a variable width profile added to the stroke.
There isn't a special "mode" to set up. Illustrator is ready to go, however there are many ways to customise the user interface to make various common controls and panels a bit easier to find. There are some presets for layout of the user interface at the top right hand side. Examples are: Essentials, Essentials Classic, Layout, Painting, etc. This will set up the panels to make these tasks a little easier.
Now, all that said and done, probably best to forget drawing freehand with a Wacom, at least for the moment, or until you are more familiar with the software. And after learning the basics and the user interface, instead try to concentrate on learning Illustrator's main tool - the Pen Tool. Understand that tool, and then learn the concepts of Bézier curves, anchors, strokes and fills, and you will be at least 80% of the way towards mastering Illustrator.
And lastly, if you previously used Photoshop or a similar raster image editor, then you can basically forget almost everything you learnt, because although they might superficially have similar interfaces, that's where the similarities really end.