1. I will probably use some kind of detergent to clean the brine tank but will rinse thoroughly. Will this be okay?
+1 on the white vinegar. Don't hesitate to use some at full strength to get the really stubborn stuff off.
2. Is there any pump suggestions?
I've heard lots of good things about MagDrive pumps.
3. If I hook a garden hose to the pump, will it contain harmful chemicals? I have an RV hookup hose I could use. Would that be better?
+ 1 for the RV hose. Your local home improvement store should carry potable water hoses that will also work.
4. Should I put a powerhead in the conditioned water storage tank to move water around, or is that not needed?
I wouldn't bother with a powerhead for the storage of fresh water.
5. Should the conditioned water set for awhile before moving to tank? If so how long?
Properly conditioned water doesn't have to sit at all if it's near the tank temperature.
6. Some pumps I looked at seem to pump pretty quick, I was curious if there was a way to slow it down if I needed to. I am assuming a dimmer switch would hurt the motor. Would putting some kind of control valve in the plumbing hurt it?
If you need to reduce the output of the pump, add a tee to the return line. Put a valve on one leg of the tee and run a hose back to your storage tank. The tee will split the output, sending some water to the display tank and some to the storage tank. Use the valve to control the ratio.
7. Any other thoughts, and/or suggestions?
I will get some pics here soon of my tank. Thanks everyone.