reply to baffled
Re: Hot water heater leaking from base? I had the same type of issue. I would often find water around the base of the hot water heater. I finally discovered it was coming from the discharge pipe (long pipe on the right side of the water heater). We changed the hot water pressure valve thinking it was faulty but it wasn't as it continued to happen. We then discovered that our water pressure was too high so the plumber put a water pressure expansion tank in line with the water heater which resolved the problem.
You can see if the water is coming from the discharge pipe by putting a small container under it.
It doesn't explain the water softener (never had one of those) but perhaps it gives you something to look at.