Yes, it is quite expensive, and should be used, when its use is necessary. In your case the use would be unjustified.
Nope, the same texture applied to multiple meshes does not slow down anything. It is the number of individual meshes, that causes the slowdown.
Depends on granularity of the assets. It is always a balance, where on one part you have number of meshes, and on the other part you have culling efficiency. On your screenshot, the modular parts seem like you would not need to consider merging them.