Small Office Network Question

I hope this is the right place to ask this. My small office was rewired about 6 years ago with Cat5e to all the workstations. We are about to upgrade our internet package to Gig speeds (1,000mbps). I have already purchased a modem and router to support these speeds, and I know Cat5e supports them as well. Our network switch also supports these speeds. All of the hardware is a Netgear product.

Question(s) 1: will we see true Gig speeds at each work station? Or at least close to them? Is it worth the cost to have the office rewired with better Cat cables (6, 7 or 8) — its an office with 15 workstations and we do have VoIP.

Question(s) 2: If the Cat5e is hardwired to the stations (at the outlets) does using a better Cat cable (6, 7 or 8) from the outlet to the workstation improve speed, bandwidth, noise reduction, etc.? or is the connection limited to the Cat5e capabilities since that is what the outlet to the network switch is wired with?

Thank you for any and all info on this!