I've gone to Christmas at Kew twice now. It changes every year and every year it is absolutely fabulous.
The Victoria Gate is the main entrance and it is the one I have used both times. I really can't answer the part of your question about the Elizabeth Gate. I have always gone to Kew by tube and then walked the few blocks to the Victoria Gate. Restroom facilities, food booths and the gift shop are located here.
Arrival is timed, but there is no time limit or forced departure. (well, maybe at the end of night ) There are food stalls available at the Victoria Gate and throughout the Gardens. People often spend a fair amount of time. It has been about 2 hours for me each time. There is a marked path that you follow (one direction) through the gardens. There are lots of people, but they are usually moving and moving at their own pace. I have always gone for one of earlier entry times so I am not sure about what the later times feel like.
Strategies: Get tickets early. Sounds like you are right on that! Bring a small flashlight. There are parts of the path that are quite dark and difficult to see in places. Use the restroom upon arrival, it won't be as convenient after that. Expect to have fun!
What I love about Christmas at Kew (besides the fabulous displays) is that I feel like I am taking part in a British Celebration with many locals, not just tourists.