Leave water on ?

OP wrote:
I know I am suppose to leave the black tank closed and the gray tank open.

This is incorrect. Don't leave the gray tank's valve open. Along with the sewer fly comment mentioned above, it is always good to have water in the gray tank when it is time to empty the black. You empty the black first, then the gray so it flushes particles from the hose.

Consider buying a waste water tote - Barker with pneumatic wheels comes to mind, when camping without a sewer connection. The gray tank fills a lot faster than the black. We can go for over a week without draining the black tank. That doesn't mean to skimp on water usage when flushing the toilet though, as solids can build up on the bottom, and you don't want that.

As far as leaving the water on when gone, if it gives you piece of mind, then go ahead and turn it off when leaving. When first turning it on, be sure that all faucets are turned off as you don't want a waterfall in the bathroom - don't ask me how I know this...

The pressure regulator is a good idea - get a good one from Lowes. I also use a inline water filter - Camoco I think. Purchased at Walmart.