Would Upgrading to 16GB RAM be Beneficial?
Looking at your memory usage you don't need more RAM.
To answer your questions:
Apps may open faster if you are running lots of heavy duty apps, like Photoshop, Xcode, etc…
I doubt you'd see much of an increase in the FPS in games. That depends on the video card and how well the game is written.
Overall performance increase would probably be minimal. The biggest bottleneck is if you are running off a spinning disk, upgrading to an SSD would probably be the biggest performance gain, depending on what you use your computer for.
If you are using many programs at the same time e.g many browser tabs and you are left with little free RAM then yes, you will see performance increased.
It really depends on the usage. I can't work on a computer with less than 8GB of RAM (many, many chrome tabs, iTunes, and 3-4 programs open at the same time). But many people are OK with 4GB.
Yes, it seems that from your screen capture you do need more RAM.
From the Apple support pages:
Tip: Page outs occur when the Mac has to write information from RAM to the hard drive (because RAM is full). Adding more RAM may reduce page outs.
So it seems that you're heavily maxing out your RAM. Check this value and try to determine when you're out of RAM, it could be a one off, but if you're always in the GB definitely upgrade.
Keep in mind that it won't be reset until you restart your computer, it's cumulative.