The speed of downloading static contents is 100% decided by Coral servers. Depending on the server status, sometimes it may take a bit longer for the contents to be downloaded. If the performance is not satisfied, you may want to enable the plugin in certain peak times only.
There should be no need. If the stylesheet got rewritten and is served through Coral, all relative (most commonly) background images defined inside it will be pulled from Coral servers too.
Looks like a plugin conflict. Try disabling your plugins one by one to find out which caused the problem.