From the example it says to use 4048 x 2000 for a background. If you can, is it better to use smaller and have them repeat? If you want the background to just repeat and play on a mobile phone or tablet, would 2k by 2k save much space?
using this large of a background for mobile is not a good idea. It would be much better to have them smaller and then have them repeat. Due to how images scale up for mobile phones, Even 2k by 2k would round up to 2048x2048, which many phones can't even hold that amount of resolution in their RAM. i would try to keep everything within or under 1024x1024, I've had soooo many problems with anything larger than that. Mobile devices only render images at a power of 2, so everything rounds up, for example: if you have an image that is 1024x64, phones will store it in memory as an even power of 2, so they would store your image at 1024x1024.
(Someone correct me if I'm wrong on this next one, but this is what I've been told on numerous occasions ) If you have an image that's 1026x1024, it will round up to the nearest power of 2, which would be stored at 2048x2048 in your phones memory, therefore taking up an incredible amount of space. So if you're developing for mobile, be very careful with your native image sizes. (native being the actual raw image, and not what is edited/scaled/resized within the game layout)