I bought mine off ebay from a seller titled: sunshinehope. The oil and Spectracide Triazicide you can get from Lowe's or HD.
Keep them dry, sealed, and cool and it will last many years.
As far as your sprayer is concerened, it may be okay for a while, but two of the chemicals are wettable powders. I have a backpack sprayer with a diaphragm pump which is made for wettable powders. Give your gallon sprayer a try and see how it does, but it may clog. Also, I gown up completely with overalls, goggles, and a respirator just to be extra safe. Plus, I now have a little one running around and I don't want to take any chances. Try it next spring and shoot me a message with your results. Make sure you let the petals from the blooms drop so you don't hurt the bees while pollinating. Fruit trees are a lot of work, but I'll bet that you will see a big difference if you follow the schedule. Good luck.