Can these posts be removed to open up this staircase railing?will I have to reinforce this beam? If so how would I do that?

We don’t know the span of the beam or the size of the beam or the actual load on the beam, but it appears that it was designed to have the opening in the wall because:

1. Single top plate.

2. Sole plate is not pressure treated indicating the entire wall was added later by a person not familiar with construction or knew it should be removed later. (The other sole plate in the picture is pressure treated, indicating that wall is to remain long term. )

3. The three posts on each end of the post do not sit on the sole plate, but rather extend through the floor (presumably to a support below). It appears there is just the top of a post base visible on the left post.

Neither triple stud posts have a post cap. I’d add one on each.

I’d also leave the double stud at the bottom of the stairs so you can turn the partial height wall horizontal and install a handrail.

If you give more info, like size of beam, span, etc. it could be determined that the beam is adequate or needs reinforcement.

Edit: Just to be clear, your question asks about removing “posts”. Those are “studs” you’ll be removing not posts. The triple studs at each end of the beam are posts, and they are to remain.