1) The crystals are most likely deposits left from the evaporation of water that used to be in the tank (as you mentioned, you had the lid off). As the water evaporated, the dissolved minerals transitioned into their natural crystalline structure, which is attractive to the dissolved minerals -- rinse and repeat and you have a larger crystal structure adhered to the wall.
2) You could -- but from the look, my personal preference would be to empty it and give it a good and thorough cleaning.
3) A thorough cleaning once a year is often recommended. Is it necessary? Maybe not, but it couldn't hurt anything either. I'm sure your owner's manual outlines a deep cleaning procedure, but if not, there are a number of resources on the internet.
Regarding the disinfection -- I would follow the manufacturers recommendations. You should use a fragrence-free bleach. Store-brand bleaches often have less additives than Clorox, which is good when the use is "food"-related. Clorox uses additives which aid in the removal of soils (things like caustic soda, soda ash), surfactants, and other ingredients to help prevent stains (sodium polyacrylate). 4 oz does seem a bit much, but the manufacturer would know better than me what should be used.
4) I'm not sure why your manual does not recommend the mixture of potassium chloride and sodium chloride -- these are mixed in water softeners quite often to decrease the saltiness of the drinking water and save a bit of money. My vote is, when in doubt, follow the manufacturers recommendations -- they only spent millions developing the thing (of course, they would also like to make money when you need to replace it, so it's a bit of a double-edged sword).
Resin in softeners is typically only good for 10 years, and after that has to be rebedded (replaced).
1. Empty the old media from the tank
Turn off the water supply and relieve pressure on the softener (easy way is to manually cycle the valve to drain a couple times until you don't hear water moving anymore).
Disconnect the softener, and bring it outside. It is filled with water and quite heavy -- you might need two people. A hand cart is especially helpful. Be sure to grab the softener itself, and not the brine tank which sits off to the side (the part you put salt in).
My dad used to own a water treatment company, so I've done this many, many times. The way we used to do it was take a large plastic garbage bin, with a large bag in it, and basically just pick up the filter and dump it upside down quickly. The water in the tank would help get most of the media to come out, along with shaking it a bit (think along the lines of getting ketchup out of a glass bottle). Once all hte water is drained out, keep it upside down and use a garden hose to flush out the rest of the media and clean it out.
We used to then just take a screwdriver or knife and poke holes through the garbage bin and bag to let it drain, but of course this wrecks the bin (we had several of these, and they'd be good for hundreds of rebeds before falling apart). Be creative so you can drain the water and then dispose of the used media.
2. Prepare the tank
Install the stem back into the center of the tank. If the stem or distributor basket (intake on bottom of the stem) is damaged in any way, you'll want to replace it.
It's a very good idea to cover up the top of the stem with tape so nothing gets down inside (could jam in the filter head later, causing lots of problems).
3. Fill the tank with new media
Put some small pea gravel in the bottom, usually enough just to go an inch or so over the basket, but the manufacturer should have specific recommendations.
Next, install the resin. Again, the manufacturer should be able to list the specific type and quantity needed. If I recall correctly, it should fill up to a foot or so below the top of the tank.
4. Reinstall the tank
Bring tank back in the house, and hook it back up. It's a good idea at this point to check all o-rings too, and put silicone o-ring lubricant on them to prevent them from drying out and make it easier to reinstall.
Don't just turn the water on full-bore, or you risk stirring everything up inside. Instead, open a tap somewhere downstream (or set the filter to drain), and then slowly open the supply to let water trickle in. Once you see water coming out of the tap or going to drain, it's full and you can open it all the way and put the filter back into full service.
Best Answer
"Iron Reducing Bacteria" create energy by oxidizing soluble iron in the water. In the process this creates insoluble iron which settles out and leaves iron staining. The bacteria themselves create biofilms or foamy messes in several areas, most notably toilet tanks and water heaters. Look in your toilet tank, if you have similar foam and iron staining you probably have iron reducing bacteria in the water.
If you do have iron reducing bacteria you have to deal with them at the source, your well. Generally this involves pouring bleach or another sanitizer down the well, pulling and circulating that through the plumbing system and then letting it stand in the pipes and well for 12-24 hours. This is not a permanent fix, but it can get you a few months respite. Any well company can assist with this process or you can find information online.
The problem is your water softener resin beads will be destroyed by this process, normally the water softener is bypassed during sanitization. You need to sanitize the plumbing system separately, and clean the water softener by hand. I recommend replacing the resin beads and sanitizing the resin tanks and brine tank at the same time.
A more expensive but permanent solution is to install water treatment systems to deal with the bacteria. Usually this involves chlorine injection, some contact time in a tank to kill the bacteria, and then running the water through a filter or reverse osmosis system to remove the dead bacteria and most of the chlorine. This is very expensive.