@iphigenie: You can't set up IDM to download all filetypes belonging to a specific category automatically but you can ask it to download individual filetypes automatically. So all that needs to be done is copy-paste all of a category's extensions to the "download automatically" box.
The only catch is he would have to add or remove individual filetypes as and when he modifies a category as the two are not synched. Besides, I'm not sure the OP was asking for this exactly.
@Earthcoder: The first feature as you mentioned is offered by your browser itself.
I realise this is a bit of a cop out but the simplest workaround for the second would be to use a dialog box extender so you just have a dropdown list of category based folders and don't need to browse your computer.
The third (website based downloading) is a bit tricky as it could conflict with the first rule. You need logic on the lines of mail filtering rules that lets you decide which rule gets priority - filetype or website - it would be hard to come by, if it exists at all.