Faux stone will look just like the name suggests: fake. I say, "when it comes to stone, just say no to faux."

With regard to covering the LVL beam, you can create a pretty good looking fake beam if you use continuous lengths of wood, and miter the corners. You can cover the post in a similar fashion. If you can't get lumber in the length you need, then make sure the joints fall over the post.

With those low ceilings (less than 8'?), I would wrap the beams with drywall.

Drywall to not bring any more attention to them .Please no shiplap anywhere .rela shiplap would never be good in a home it is meant for th outside of a barn or shed. Do not get caught up in the Joanna Gaines world