To properly adjust the headset you really need two 32mm headset wrenches or one HS wrench and big adjustable.
Yes you will need a washer to makeup for the missing reflector bracket.
I would just overhaul the HS at that point and maybe put in new bearings.
There should be a minimum insertion or max height mark on the stem, you want to be sure that is below the top of the nut.
Put the clamps where ever they need to be to make the rack as level as possible. Front racks don't tolerate alot of weight (handling) and slanted one attract attention.