Those are good places to start. With out sending your water off to be tested professionally I'm not sure how much more you can really test for. If you have a pool place near you, they may be willing to test your water for a small fee. If not you may need to do a search online for a place that can test your water and tell you everything that is in it.
NitrAtes, Phosphates, Hardness those are things I would look at. You can also get a TDS
meter (total dissolved solids) and see what's going on with your water as well. Do a google search for TDS
meter. They are not very expensive and a good thing to have anyway.