It sounds like you really don't know anything about how water actually works, and are thinking about it as being sort of like actual water. This will get you into all kinds of trouble. Read the Hydrodynamics Education thread in my signature; it will tell you exactly how to expect water to behave.
In response to your specific questions:
I'm wondering - will things left in the path of the water diminish its pressure or slow down its tendency to flow?
No. Water movement is instantaneous. The "speed" of pressurized water is solely a matter of the number of water tiles which are teleporting through the system. You have a volume over time but not a velocity.
I want to drop the water down 7 z-levels, then up five, then down five, then back up again and back into the river. The wiki says that water will only go up to one level below the original height. So if it drops 7 levels, I can only expect it to go up six, right? But the real question is: After going up five levels, will the water still want to go back up the 6 levels, or, after that, will it only act as if it had fallen the 5?
Water doesn't go up at all except when pumped. It can merely go
down to any space to which it is connected by a path of 7/7 water tiles. When you ask about how the water will behave after it's fallen a certain distance you're asking the wrong question. The water that falls into your pipe does nothing on its own; it sits there and creates a path which other water can use to find destinations.
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