From what I've read the water softening systems intended for home use will not benefit your aquarium and indeed might hinder what you wish to achieve.
As for testing the tap water. I would let a sample sit in a shallow container for a few days and then test the ph. This will give you your true ph value. Most say aquatic plants prefer soft and more toward acidic. However I have several "sensitive" species that are thriving with a GH of 8 and a ph of 7.4
Also if you add co2 this will drop the ph considerably.
I really think most fish will acculmate to what you have when the exception of discus. If you really wish to keep them invest in an RODI. They must have soft, acidic water, with high temperature.