Is it necessary to clean every record?

It's up to you. The least that could happen is that you will get some crud on the stylus (just clean it off) and the worst is that their will be "hard" particles in/on the LP that will damage it, however slightly, when played.

New and seemingly unplayed LP's are usually very noisy when played without a cleaning from my experience (there is some kind of white/light powder in the grooves and on the surface).

Maybe try a good "hand held" wet brush and a dry carbon fiber brush if you don't feel like using the machine (this is easy to do while the LP is spinning on the table)? I do this often when I get home and want to listen to a new purchase that looks fairly clean (no boogers and such:-). I zap it with a Zero/Stat, run the dry brush, run the wet brush and end again with a clean dry brush (30 seconds tops).

Why have a VPI if you're not going to clean each new disc. I spend 2-3 minutes per disc for a thorough wash and rinse with that machine.

Yes, it is.

Only if you're obsessive compulsive. I clean records that appear or sound dirty. It doesn't always help, but at least I give it a try. With brand new records, I don't usually clean them before listening(I know, burn me at the stake). If I don't like them, I'm not going to keep them and it seems a waste to spend time cleaning them until I'm sure. By the way, I use a Nitty Gritty 1.5FI and it takes me a minute and a half max to clean both sides of an LP.

Not only every record but everytime it's played. At least in my experience this gives the best long term results. any dirt, even surface dirt, can be ground in by the needle. If the record is cleaned befor play this reduces the possibility of this. To me, it's less of a sonic benefit than a long term, record lasting benefit (as records are expensive and sometimes difficult to replace). Some people use a carbon fiber brush for the "in between" deep cleanings. This dry method gets rid of most of the loose dirt, but I still prefer using the machine to clean each time--I guess it is obsessive compulsive at that point.