It rains, it snows, water temperatures change......as long as the temperature change is gradual. When it rains, it rains on everyone's pond.
As to the muddy water from your patio area, where's it coming from? The stream bed should stay relatively clean with constant flow over the rocks. If you don't remediate the source of the mud getting into the stream bed, then the flow will merely drive the majority of it downstream to collect on the bottom of the pond. Then you'll have to clean it out. Doesn't make sense. Fix the problem at the start, not at the end.
As to pumps, a simple calculation is as such : If the head (top) of your stream is 50' away from the pond, and the land rises 6' during the course of the 50' run, you've got what's about 8' of head. If the total volume of your pond is, say 3000g, then optimally you need to move half the volume of the pond each hour. So, theoretically you need a pump that's rated for about 1500 gallons per hour. However, because you're "lifting" the water about 6', the pump won't deliver that much water. Off the top of my head I'd say that you need a pump somewhere in the range of 2700-3000gph. Check my figures, but for each foot of "head" the "gph" of the pump decreases.
I don't know the total volume of your pond, nor the GPM rating of your pump, but if you're losing that much water in an hour, then you've got a decent-sized leak somewhere. There's a hole, a fold, a low spot......take the stream bed apart. Re-lay it with no rocks. Run the pump hose to the top. Mark the pond level. Run the pump for 6-12hrs, check the pond level. If you're losing water, it's pretty well guaranteed that it's from the stream bed. If you haven't lost any, then you've fixed the problem and can re-lay the stones to your liking.
I wouldn't bother trying to "fix" someone else's work, because you don't know how it works. Better off to tear it out, re-use what you can and put it back together so you understand how it's built. It's much easier to troubleshoot something you've built than something that someone else has cobbled together.
Now, when you say your pond is "pre-formed", do you mean a rigid kiddie pool pond (as in ABS), or is it a hole with a pond liner? What are the dimensions (length, width, average depth.....guesstimate)?
If you plan it out, do it right, get the proper pump, filter, etc., there's no reason that this can't be a great build. The location looks great.
Tell you what, I'll make you the same deal I made Priscilla, buy my airfare, bar bill, food, laundry and I'll come down and do it all for you........wait a minute.....cancel that.....Priscilla lives in the Cayman Islands, you're in North Dakota.