You’d be entirely correct, and that’s exactly why there’s an ongoing debate in physics and cosmology as to why there’s so much matter, and so little antimatter in the universe.

(Do note I’m not an astrophysicist, so this may be a bit wrong, but I think the main part of it is right.) Not exactly. Everything in the universe is constantly drifting away from everything else. The reason it is pretty much only visible at the scale of galactic clusters is that literally every force in the universe overpowers this expansion, unless the distances between the objects are truly absurd, in the range of millions or billions of light years.