Hi & welcome! Yes, it looks like Ficus benjamina. You may already know and this plant just didn't get the attention, if you want symmetrical plants, rotate them often. It can be difficult to keep them even inside. A lot of my plants are uneven on purpose, just depends on someone's preference for a particular plant.
Braiding is fine, or spiraling, tying in a knot. There's no reason not to, but if the branches of the pictured plant are manipulated to be more upright, the top of the tree will be too tall to get enough light on most of the foliage.
This plant could be rejuvenated by trimming. I would go as low as the red lines.
Beware that when you cut into a Ficus, white latex sap will leak from the wounds. It can cause a rash if your skin is sensitive, and can stain the floor or fabrics.
Best luck with your move!
