I seem to remember reading the only lab in the UK that was producing prints for cinematic release closed, so all prints come in from overseas now.
Never seen the point of 35mm now we have 4K. It simply doesn't look as good. 70mm and IMax might have more going for it, but does it look better than decent digital projection? Different yes, but for me, the jury's out on the technical quality.
Our local cinema had a satellite based connection for movie download. It must have taken an age at those sort of data rates! They are now on a fibre connection back to the exchange and the whole projection operation is a sealed set and forget system. There's a volume control in each theatre hidden behind a panel, but that's it. The projection floor is a corridor about 7' wide with air con and 6 Barco Series 4 projectors. They are linked to a central video server and remote diagnostics and that's pretty much it. The amplifier room is common to all screens and again is fiddle free, with no visible controls, just a wall of quietly humming amplifiers and processors!
Each cinema has a local connection panel that provides HDMI @ 1080p max plus stereo sound into the associated theatre. When they do a corporate hire they have a pair of 10" PA speakers and a little rack that they wheel in containing a mixer, a couple of radio mic receivers and a stereo amp.
All very simple and tweak proof and not at all like the generations of "proper" projection!!