Welcome in advance to Texas, @Phil Monkhouse! Have you heard of City-data.com? They have lots of demographic data that is helpful in evaluating an area.
Lake Olympia http://www.city-data.com/zips/77479.html
Sienna Plantation http://www.city-data.com/zips/77459.html
1) Before all these nice housing developments moved in, Missouri City was a somewhat low income area. If you look at home prices on Zillow, you'll see that the homes north of Hwy 6 and east of the Ft. Bend Parkway are much less expensive. My guess is that parts of Sienna Plantation are zoned to the same schools as the homes in the older part of Missouri City. I don't know that for a fact, but I do know there are lower income neighborhoods that are near the more upscale ones in Missouri City, so that may be what's going on with some of the schools. Most of Missouri City is very nice, though.
It's not that the schools in the lower income areas are not funded at the same amount per student as other schools in the district, but kids growing up in poverty sometimes have stuff going on in their lives that can affect how well they do in school, and there is often a higher incidence of violence, drugs, etc. in those schools. If the kids score poorly on state tests, the school will receive a lower ranking. Generally, lower school scores mean there are more low income students attending that school.
2) On average, I believe you'll pay about $12K per year for private school.
3) Yes, people will pay more to live in areas with better schools if they can afford to do that. This is something that real estate investors must consider when evaluating properties. When you are looking at potential homes, you should look at the particular schools to which that home is zoned.
4) Good schools can go down, and bad schools can come up. In general that will be directly tied to what is going on in the community. If a community is growing and new housing developments are coming in, I'd expect the schools to get better, too.
All that said, you might want to also consider Sugar Land, which borders Missouri City. Median household income in Missouri City in 2012 was $84K and in Sugar Land it was $113K. You still need to check the data on the individual schools, though.