Can this be done? Like requesting images on the forum? I imagine that'd lead to clutter, but I've never really read into how requests are allowed on here.
I have a request I'd like to make of course, but I won't bring it here at the moment.
Requests are not allowed period. Unless you mean series or character help before you upload an image in which case just upload it and put the appropriate request tags.
Source requests for images that are already on Danbooru are perfectly legitimate, just use the source_request tag and if it's an old picture that's unlikely to be seen by many people, you can leave a comment saying "Anyone know the source for this?" as well. (Just do it once, don't repeatedly bump the picture, that's annoying.)
As far as requesting images, I don't really know what you mean by that? Like, you have a low quality image and want to find the original version? Something like that? Or are you asking for "images of X and Y doing this and that" type requests? Either way, we don't really have a facility for that.
You can try tineye if you have an image and are just looking for a higher resolution but that's kind of a crapshoot for anything anime. IQDB works much the same way but will search the various boorus.
SauceNAO can help if it's from a manga, doujin, magazine, pixiv, etc. iisearch will find sources of eroge CGs. And I'm not sure what the hell http://details.kemuri-net.com/ does or how to use it (You enter the image's MD5 hash, and then....???) but it's linked from iisearch so I figure it might be useful.