The corkboard background will tile, so if you are just looking for a grid you can make it pretty small… a single square from your grid if you like… and it’ll work.
Far as I can tell from the pattern, the corkboard is a 512 x 512 px image which gives a good size for a “random” image tile without starting to look too much like it’s repeating.
DPI… the image is going to be used at 100%, so the resolution doesn’t need to be any better than the best monitor you’re going to be viewing it on. Just make sure it looks good at “100%” and you’ll be fine.
Scrivener will load up the pattern file each time it starts, so you should put the image file somewhere where it’s not going to be disturbed. I suggest the Resources folder within the Scrivener application folder itself.