Polyacrylic can be used, it is a water based polyurethane. Being waterbased it should not darken the finish.

Generally Satin finish does not have much of a shine, I have used it on my interior trim and it has a very slight sheen. Have you tried to reduce the sheen by rubbing with steel wool?

Rustoleum makes a Matte waterbased Polyurethane, link below.

Here is a link that might be useful: Rustoleum finish link

Assuming you're using clear poly, generally oil based poly will bring out the wood color somewhat which is the opposite of what you seem to have observed. The finish will yellow over time but I doubt you would have observed this in a short period of time.
I'm not sure what you consider shiny. Satin oil poly is not shiny but if it's too shiny for your taste there are duller oil based finishes. It's important to stir the poly thoroughly because the flatting agent settles to the bottom. You can also pour some of the poly off the top before stirring to get a duller result.
I like the oil finish since it's tough, easy to use and dries slowly allowing time to apply uniformly. The downside is that the longer drying time can allow time for dust to settle in the finish.

VERY lightly sand with a very fine grit sandpaper, then clean with furniture polish Old English.

As said above, and oil based finish is going to give a darker/amber color. Water based finishes will not darken or color it as much, although some color change will occur. Satin should not be shiny, my guess is that it wasn't stirred enough. You can knock the gloss down with fine (000, 0000) steel wool. Stay away from all off the shelf furniture polishes (Old English, Pledge, Liquid Gold, etc.)