Have to take the trim plate off the shift selector to get at the bulb. Could possible be the wiring got pinched - have to open it up to see. There should be some pretty detailed directions on this forum - but here is a shorter version on Toyotanation that I ran across on a quick search:
http://www.toyotanation.com/forum/132-9th-generation-2003-2008/386764-how-replace-2004-corolla-shifter-light.html
As for the washer pump system - that is pretty unusual to not have that already installed on the car, unless it was specialty ordered without it or was removed due to some other modification/accident. Easiest way to get one is to hit a salvage yard and pickup any 9th gen washer system (control stalk, pump, fluid reservoir, tubes, nozzles, etc.) They do have aftermarket ones as well - be my second choice if I couldn't find an OEM to install.