The setup of the moons would mostly affect the tides. Instead of a nice pattern of tides twice a day, you'd get a much more irregular and complex pattern of tides spaced oddly and of different sizes. Maybe you'd see some increased tectonics as well, but not likely to be much.
With the two suns, you wouldn't see much effect from the farther one. It may increase the average temperature of your planet by 5-15 C, but that's about it. If it's far enough away to mostly be just a bright star, then nearly all its heating and lighting effects will be too small to notice.
That's all that should be affected. Magnetism, north pole, seasons, and weather should all be pretty much unaffected.