My question is, how should we go about sanding/smoothing out the uneven chipped wood so that it can be perfectly level
It looks to be unlevel for the entire length of the board, correct?
Aside from smoothing out the jaggies I would advise against tackling the entire length of the board because you are more likely to make it worse than better.
and so then we can install a (likely) load-bearing wall along the beam probably in between our 3 posts?
Sorry, this is nonsense. The two red posts are load bearing and hold up your house; notice how they are set on a concrete footer?
You are most likely not qualified to put up a load bearing wall so if you add a wall in between the posts then it is effectively a non load bearing wall.
However, I am a bit confused/worried about that jack post in the middle. Those are typically considered temporary. The most common use case for those would be to support a heavy static load like a large couch, entertainment center, or cast iron tub.
Would a belt sander work, or would we need a random orbital sander, or is there some better way to do it?
Either choice would be excellent for smoothing out the jaggies.
For leveling out the entire board, I would expect a circular saw to be used.
We don't have to do it ourselves, we could have contractors do it, but we're kind of just wondering the recommended tools for doing this to make sure it's done properly.
Yes, ask the contractors.
I am confused as to how that proud beam board prevents a wall from being built.