It entirely depends on one preference. Although I appreciate good mechanical keyboard, I can't say the same about multi monitor setup. For long years I was saying "the more monitors the better" but after a while I realised that I am more distracted with 2+ monitors. For me large monitor with high resolution, preferably, ultra-wide plus spaces/virtual desktops in the system is the best solution.
Buckling springs are always noisy (you can reduce but not eliminate the noise by putting vibration damping materials inside the springs). "Clicky" switches like Cherry MX Blues are always noisy. Other key switches are much quieter, and most of the noise comes from operator error. You're not supposed to press them all the way down like a membrane switch. The operating point of mechanical key switches is near the middle of the travel. If you press too hard they'll bottom out and make a lot more noise, as well as tiring your fingers more. If you're prone to doing this by accident you can fit soft o-rings around the keycap stem to cushion the end of the stroke.
The problem is "buying it wrong" a seller like wasdkeyboards (or others) has dropdowns for half a dozen types of Cherry brand switch and a couple dropdown options for sound dampening o-rings.
At home I use an original model M and I'm quite happy with it and frankly it just isn't that noisy. If people don't like the noise, the problem is they're packed in too closely; perhaps my loud breathing also offends them if they're that deeply invading my personal space.
I could never do that. I use 3 monitors (if you count the laptop) and I'm way more productive with it. I have low-priority windows that I need to have opened (a terminal, a console log with 3 tabs of its own, simulator window) and that is a mess to handle if I have to actually switch between them. Virtual desktops help a bit but still cause a little strain every time I have to switch from one context (development or checking the source) to another (testing a mobile app and checking the log).
I thought so, then downsized to just one monitor, and that was pretty great. When I move around, working on just on the laptop doesn't really impact my productivity that much, unless I'm in a deep debugging session, but I think a larger screen will help with that (I use a 13" Retina right now)
Personally I find great to have a full screen editor/ide without floating file list and symbols one one monitor and documentation/shell on the second. When you look at one you are not interested in the other so I would not call it multitasking but easier process switching.
People who keep the mail client open should try notifications: events versus polling is much more efficient for low clock human beings.