Does building cooldown reduction (CDR) lower the cooldown between a player using the same tunnel twice?
Does it lower the cooldown of tunnel usage? Yes and No.
Building cooldown reduction will lower the cooldown on your tunnel building skill. However it will not lower the cooldown on existing tunnels. You'll always have a cooldown of 10 seconds for going through a tunnel that's already there.
Despite the fact that it won't reduce the CD on existing tunnels, you shouldn't hesitate to pick up one or two CDR Items on him. CDR scales extremely well with Rek'Sai since he has absolutely no spell costs.
No, because the usage depends on each tunnels on-target cooldown (which are not affected by CDR)
The creation of new tunnels is affected by CDR