Type 3 fonts can use everything Postscript can (oh, perhaps not issue an "endpage"). But support for these is rapidly dwindling -- if not already entirely gone --, as it requires the font-using software to implement an entire Postscript interpreter.
You are mixing up various parts of font technology, by the way. Postscript fonts do not use "Postscript Level 2"; they use a (very limited) subset of the original Postscript. Not a single Level 2 feature anywhere. The "Type 2" of CharStrings have nothing to do with Postscript levels.
There are good reasons not to use line widths in a font, as a fixed line width would not change with the point size. There is a font Fill type that was meant to have single strokes as font definition, but the problems with these were so great it has also been removed from the official specification years ago.
If all you want is train yourself with Postscript (and not particularly with fonts) , you should find a download of GhostScript. I learned Postscript programming by talking to a LaserWriter using modem software, but its modern variant, Acrobat Distiller, doesn't come with interactive features. If I'm correct, GhostScript still does, meaning you can interactively build up anything you like and see it appear on the screen.