a lot of mappers use background images from sites like pixiv, so is it possible for a background image to get dmca'd even if you credit the artist? and if so, is it safe to use background images from pixiv and other art sharing sites?
You should ask the said artist first before using the images. Some can't be bothered to reply your messages, so you should look at their profile too and see if they allow you to use it for noncommercial purposes.
Using and submitting a beatmap assumes that everybody has the rights to use said music, art, and elements of the beatmap, just like Ryu Sei said.
Though, if you don't then it is not punishable by osu!, but the content you posted can and will be taken down. It is a much more lenient process with the backgrounds though because they can change the background easier than you might think, but it is in your interest to get the rights to use just for posterity sake.