Like hydroservice said, every hydroseeder has a tank capacity rating and a working capacity rating. The tank capacity is the amount of water it would take to fill the tank to the very top. The working capacity is the amount of water you put in the tank to allow room for materials. If you were watering a lawn, you could fill the machine to it's full tank capacity, however, if you were hydroseeding a lawn, you would stop at the working capacity and the rest of the space would be taken up by mulch, seed, fertilizer, lime, etc. Once those products are added to the tank, it would raise the overall level back up to the top. If there is still room to spare, you could top the tank off with water if you wanted.
Regarding paddle agitation and liquid recirculation, almost every paddle agitation machine has a bypass line plumbed from the pump back to the tank. This is called the liquid recirculation line. It is used primarily on applications where you are spraying from the hose. If you are out at the end of the hose and you need to shut off the valve, then the material being pumped has to have somewhere to go. The liquid recirculation line bypasses that material back into the tank. If the material didn't have anywhere to go, there would be issues with blowing hoses or excessive heat buildup in the pump. The liquid recirculation line is also used to help keep granular solids like fertilizer and lime in suspension.
There are two basic types of hose used on hydroseeding equipment. Semi rigid hose keeps it's shape when coiled on hooks on the side of the machine or on a hose reel. Because of this, you are able to pull off the amount of hose needed to reach the area that you are spraying. You don't need to pull all of the hose off of the the reel if you are spraying an area relatively close to the machine. The other type of hose used is collapsible hose. Collapsible hose needs to be completely extended before it can be used. When the pump sends material to the hose, the pressure expands the hose and allows the material to flow through it. If left partially unrolled, it would prevent the hose from being used properly. With collapsible hose, you also need to purge all of the slurry from the hose prior to coiling it back up to put it away. It is not designed to be coiled up with material in the hose.
Hope this clarifies things a little better for you.