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).
I only see one valve, incorrectly installed in the wall cavity at that, so there is no way to bypass the softener for maintenance or if a component fails. So no, its not installed correctly because a bypass is a standard part of any softener installation.
Without a bypass you are going to find that those cheap plastic components they make water softeners with are going to eventually fail and it will spring a leak. Hopefully the incorrectly installed valve you have now comes before the water reaches the unit. Then you'll at least be able to shut the water off from right there and not at the curb. However you'll then be without water in the house until you fix whatever issue your having with the softener. Below is a diagram of a standard bypass setup which your manual should also have.
Best Answer
That series was sold with and without a carbon filtering system which makes it a little harder to described. If you have a carbon filtering system (there's is called a "HYgene Bacteriostatic Filter Media" containing Silver Impregnated Activated Carbon) which is the more typically and suggested unless you have well water, the manufacturer suggests replacing the carbon filter every 3-4 years. The carbon is porous and is underneath a few levels of filter media and will hold onto the smaller particles. Also, that series appears to be fairly typical and has a salt tank filter, I highly recommend checking and more than likely filling that up. The salt is fairly cheap in comparison and the system is designed for the homeowner to maintain that themselves. The salt aids in the life of the filtration system, the filter system washes itself out and adds salt as a Regeneration cycle.
The consequences, the regeneration cycle is an attempt to clear the debris and if the media is too old or too much media has been flushed away the regeneration cycle will either stop and your water pressure will drop (would probably take months for you to notice) or the regeneration cycle will happen significantly more frequently wasting your electricity and remaining salt. The less filter media the system has, the more likely it is to get things (bacteria, hard minerals, debris) through which is no worse that not having the filter. The carbon will "bleed" and release the bacteria it was holding onto but that is just what it does and will not typically effect smell or taste for many years past it's prime if it is kept wet (which it is as long as the bypass hasn't been on since you moved in).
The systems themselves are expensive, the filter system look to be < $300 USD with installation. So you may want to look into getting it all fixed up. You'll have to monitor the salt about every 6 months but otherwise it should be maintenance free for at least 3 years.
If you are still concerned, most people install a bypass value system for maintenance of the system (an for heavy gardening, filling up the pool, going on vacation). This series appears to have the bypass installed as part of the unit. The bypass value does exactly what it sounds like, it bypasses the entire unit. Looking at the Manual this unit has a single valve to bypass (Page 5/6 manual using verbage "by-pass"). Sidenote: most home-made/plumber installs for a bypass system will have two valves, one for redirecting the input around the system and one for switching the output from the unit to the bypass.