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).
Water softeners do use water to recharge, but it shouldn't be that much. With a new filter and all electronic controls working, most systems should send no more than 25 gallons through during a recharge cycle.
The theory is that the filter media (special polymer beads, often stored in what looks like a high-pressure air tank) is "charged" with a high amount of sodium ions from the rock salt you load into the bin. Hard water containing calcium and magnesium carbonate, which are only slightly soluble and cause lime scale, comes into the filter from the house supply, and the sodium replaces the calcium, forming highly water-soluble sodium carbonate in the water supply, which won't cause scaling, leaving the calcium and magnesium ions in the filter. To "recharge", the softener fills the salt bin with supply water producing a brine, which is then flushed through the filter media. The sodium replaces the calcium and magnesium in the filter, which then hitch a ride down the drain as soluble chlorides.
The amount of water needed to produce the recharging brine varies by manufacturer and age of the filter media; this ion exchange does take its toll, as the charged ions are corrosive (a surplus of positive ions in a water solution makes the solution acidic). The softener also relies on several detectors to determine system status, that are exposed to hundreds of thousands of gallons of water over their rated life, much of it salty and highly corrosive. Over time, all these components wear out, with more or less detrimental effects on the system's overall efficiency.
Best Answer
If you are using regular, "cheaper", rock salt instead of ones labeled for water softner use, those salts contain a lot of dirt which will produce the same results you are experiencing. Part of the problem could also be from the water itself.