What is the typical PCB fabrication process in a professional PCB house?
Back when I did board design more actively, typical process was purported to be:


pre-bonded (not plated-on) copper on board material (from outside suppliers)
drill
art onto photo-resist
etch/clean/remove resiston inner layers.
stack layers (and pray that they don't spin one on you)
at some point in here mill the edge of the board to the correct shape.
electroless (nickel? or copper?) to get some metal in the drilled holes so that plating could work.
plating to get more copper in the drilled holes and connect the layers/traces at each drilled hole. Plating with tin or tin/lead to reduce tarnish issues.
Etch the outer layers here, or after next step...
Possibly masking and additional nickel and gold plating if there were gold
contacts. Talk about your hefty upcharges.
Solder resist.
Silkscreen.


Actually, it may be that they only drilled the registration holes (which may or may not end up on the final board) before etching and bonding, and drilled all the component holes AFTER etching and bonding.) I do distinctly remember a probelmatic layout (by a fancypants outside contractor with CAD!) where the registration holes for one layer were off by 0.050 inches so the holes were not always catching full copper on that layer. 

Never visited a fab house, but I designed a few boards and checked a lot more (including good old 4x photo-reduction art - who-hoo!) as well as making my own single-layer stuff. Multi-layer we sent out.

So, missing from your list would be stacking and bonding layers, and plating the through holes. On your list but I don't think it happens is plating on the copper in the first place - as far as I know it was and is a copper sheet/foil that is bonded to the substrate. In some cases it might be built up by additional plating for a hefty upcharge, but mostly it's not. Cheaper and faster to use 2 oz foil than to plate 1 oz up to 2 oz.

Solder mask was, as far as I know, silkscreened on just like the silkscreen layer - but this is also pre-SMT days so that might well be different now that things have to be more precise. Wave soldering was state of the art and all pins were at least 2.54 mm apart.