Welcome to the forums.
A lot of questions here, I will try to hit some of them (I do not have a G3).
Almost any Android can be rooted. The question is, how difficult is it. Verizon tends to lock down phones even more than OEMs, making root more difficult. I think some of this stuff can be countered without root access.
Homescreens: I would suggest a different launcher. Perhaps Nova. Nova can allow freedom to move/reassign where the home screen is. Sometimes, a different launcher can speed up a device (from what I understood, the G3 launcher was quite light to begin with).
Increasing speed: If you go to Settings>scroll down to about phone>tap build number 7 or 8 times, that will open up developer options. Back out one screen, and into developer options (should be the next entry above about device) and click on it. Scroll down till you see animations. Tick each one (should be 3) down to about half. See if that helps the speed.
Speed part 2: You can try disabling some apps that you don't use. They are probably sucking up too much RAM and the lag you see is Android killing apps to make room for more RAM to launch the app you need.
http://forums.androidcentral.com/amb...able-apps.html
Screen: The darker screen may be a counter to the screen size with power consumption. Your screen is always going to be your biggest battery drain. The less bright you can keep it, the longer your battery will last between charges. This may have been set lower at the factory.
As for the Droid or TouchWiz (TW) features, that isn't really possible. You might find a launcher that can mimic some of the stuff, but for instance, TW is a Samsung thing, and can only be installed on proper Samsung devices.
I would start with Nova and go from there. Try as much as you can before following other suggestions I made.
More info on Nova:
http://forums.androidcentral.com/amb...-launcher.html