By all means test the water. You might find that mixing some of all may give you what you want for the fish. It also depends on the kind of fish you are keeping.

However, unless you are breeding them and need to keep them in their most natural conditons to prime them for swawning, it's generally better to just keep less sensitive species and acclimate the fish to your water than to try to completely change your water chemistry to suit the fish.

Your RO water will be your best bet. Mix the RO with tap.

Some fish, particularly those that are indigeonous to South America, prefer soft (and acid) conditions. That's mostly Tetras and Discus..

It all depends on the fish kind. The levels of functioning of your water softener have also to be checked in order for you to not have any kind of problems.

Here is a link that might be useful: Complete water softener reviews