Why is the West Wing wall height 2" but the Manor and Return to Shellendrak's walls 3"? Is it because is set up for Terrainlinx? But if you don't want to use Terrainlinx, how do you cover up the blank spots/sections of the floors and walls?

It is definitely due to it being a TLX conversion and why the older set isn't offered any more.

Is there anyway to use the West wing with the original set?

I personally would utilize them is different footprints or maybe kitbash specific pieces into the 2" height. If there is a specific request that you can't handle yourself, a kitbashers around here might offer to do something and submit it.

Honestly there isn't much in west wing that isn't covered in the manor and return sets.

The only thing west wing offers is a conversion of the manor textures to TLX format.
And TLX format specifies 2' walls.