Sorry for the slow reply. The big game developer's conference is in a few weeks, and I've been tearing my hair out.
The polyline "L" is kind of a special case, as AC3D sees it as a triangle. (Switch it to polygon mode, and you'll see what I mean.) So yes, draw each as its own object to start for that case. Most of the time you don't need to do that however.
To make your object have thickness, you'll want to select your shape and use the extrude button. AC3D will add thickness along whichever axis you drag once you click extrude.
Incidentally, once extruded you should be able to unweld that corner and curve it.