Hi Dmitriy,
Welcome to the group. The cartridge in the machine is a water softener, which can be recharged so you don't have to replace it. But it seems like most people just remove it from the machine and condition their water externally. Depending on the water chemistry where you live, that may or may not be necessary.
As far as plumbing, you don't need a flojet if you can place the water tank at the same level as the machine or higher. Otherwise, if the tank needs to be lower than the machine, a flojet would be a good idea. The vibratory pump in the machine can pull against somewhat negative pressure, but not a lot.
Frank