The Venturi Towel Bar #BTB-VNC1B protrudes 2 31/32" from the wall. Below is a link to the specifications of this model for further details. https://pfisterstorage.blob.core.windows.net/documents/ss-btb-vncx.pdf
No, it is not recommended to cut or modify the unit. Any modifications made to this model is not recommended or warrantied by Pfister.
Depends if the tile is strong. It cannot be installed on drywall.