The 7000 manual has draw rate charts that you can use to properly set the correct brione draw times. Longer brine draw times are generally more efficient, but only to a point.
What is your injector size/ PSI? We can estimate the proper brine draw time based on that. Or you can simply put the system into a regeneration and time how long it takes to draw all of the brine out of the brine tank. Times that by 4 to get the total BD time. This is only an estimate and slight variations may be needed. The fast rinse is not used to rinse salt out of the system, this should be completed in the BD cycle.
As to salt residue/taste. Salt left in the system will have a definite taste that will quickly go away by turning on a faucet in the house if your systems regeneration cycle is not adjusted correctly. Spots, etc are simply a part of TDS. Soft water makes cleaning much easier, but the spotting will still occur.
If you continue to have a "salt" taste in the water after you rinse the system down through a faucet, then your water hardness/softness and other water issues may simply leave that taste in the water. Remember, this is ion exchange, you are trading calcium/magnesium for sodium.
FYI,
#1 injector draws at .35
#2 injector draws at .5 GPM.
#3 draws at .7 GPM
This should help make the math fairly easy.