as you say, you and your bike have done perfectly fine with what you did on july 4th (77 miles or 124 km is nothing to sneeze at so you must be in great shape). The hiker bkgd is a big advantage as you will be much more aware of packing compared to folks who havent done outdoor stuff, specifically when you carry the stuff you bring under your own power.
chain tool? in theory yes, but not necessary. What you will want is spare tube/s and a set of three tire irons (plastic ones come nestled into each other in a small holder) and the know-how to properly change a tube and fix a flat.
spokes--again, no real use having them if you dont know how to replace them (I dont really)--but to put things in perspective, if you keep the weight reasonable in your panniers (20lbs or so as a rough number off the top of my head) and your wheels have been checked out by a good mechanic at a bike store, then you will most likely not ever have a spoke break. If a wheel / spokes is in good shape, proper spoke tension, then the chances of problems are greatly reduced. Your weight, total weight on rear wheel, how the wheel quality and condition is, will all play a part (not to mention how your ride, do you bash over potholes, never getting weight off the rear when hitting holes, etc etc)
really the most important factor is to try to get a competent wheel person to go over your wheels, especially after you've ridden it for a while. The store you bought it at should give it a once over to adjust for the normal new bike cable stretching that happens anyway, and if they are competent mechanics, and you say that you will be loading it for overnight stuff, they should get the wheels to be as good as they can be.
I personally have never broken a spoke when touring, but I have had a wheel go out of true, its no big deal, next bike store will true it and charge a minimal amount.
If you find you really get into touring, wanting to put more weight on your bike, at some point perhaps you could look into getting a 36 spoke rear wheel that will be stronger if you have problems with the stock wheels. If however all is fine as is, hey, just use it and have fun.