Just to be clear: I was advocating a whole house filter - not a whole house warrantee. It sounds like a whole house filter is needed.
The other post about a filter AFTER the softner is also advised. I too had a "resin in all the pipes experience."
It was like thick blood coming out of all the faucets. Scared the kids to death.
I now have a filter after the softener. I also have a second regulator and run high pressure through the filters and softner and then re-regulate down to about 60 pounds. - Very nice and consistent flow.
I was able to clear the pipes by back flooding water some how... Perhaps through the kitchen sink and draining it out of the water heater. What a mess. I can't believe I was able to clear the pipes....
---------- Regarding the rust, I too tend to think it is "something else". We had a plumber do some work and later started to get rust in one tub. I was sure that he had used a piece of black pipe, but he was sure that he hadn't and had all sorts of things to blame it on.
I had the plumbing R&R'd about year later by someone else to install a shower . The rust was all caused by a 1 inch by 3/4 black pipe nipple. There rest of our house in copper or brass and there is much electrolytic action between those elements to the detriment of the iron.
Check you pipes.
----- sad news ----
I tend to think that at this point any effort you spend on this softener is a waste.
You used to have a filter, but it clogged SO MUCH that it was removed???? Where would that gunk have gone???? (into the ?softer???? YES!)
Get a coarse (25 TO 50 MICRONS) filter and leave it on. Get a big one. Change it as needed. Are you sure you are seeing IRON and not SAND????
You don't have a manual. You can't find a serial number. Can you find the brand to go to the web site? Is it a sears?
If you have some free time and If you do wish to continue... (and I advise again continuing except as an educational experience for you)....
The salt need not be removed. As I said, A hose from the hot water drain will make all the brine that you need. It will melt the rock salt just fine.
You can force recycles by moving the clock or digital timer. Some units have a "recycle now" button.
Often there is a "screen" in the softner siphon inlet. It is likely clogged base on the other data you provided.
You asked if you "have to add water" - Normally you do not. A float control and timer limit the amount of water added. BUT - since you don't know if you have brine, then you should fill salt tank until you see water flowing out the overflow drain from the salt brine tank. Then you will know you have water and brine. Fill from the top with hot water.
Then mark the height and see if water draws down when cycling. I doubt if it will. At that point you will need to clean the siphon inlet and screens.