What Mac OS are you running on Basilisk II?

Moving these files to a Basilisk II (or a SheepShaver) hard drive with HFVExplorer, they may end up on the Mac side as blank non-descript icons. The Mac Finder won't know how to deal with them in this state.

".dsk" files usually will mount OK on the desktop if you drag its icon onto a Disk Copy 6.3 icon to launch it. - ".img" files might do the same, but Disk Copy can be "picky" with its own files if they've gone "generic". Use Disk Copy 6.3.3 from here if you don't have it installed.

".dmg" are Mac OS X native and will not be of any use in a Classic Mac OS, such as in a Basilisk II (B2) emulation. You need to use a Mac running OS X to deal with these, or use the dmg2img utility for Windows to convert then mount the result as a drive in B2. [Caveat] '.dmg" files are usually HFS+ formatted, which means that they will only mount in a Mac OS 8.1 or newer Mac OS, if your B2 is running an OS earlier than this, they will be of no use to you even if you do "convert to .img".

".toast" files can be mounted in B2 on the emulated Mac desktop by using the Virtual CD/DVD Utility from here.

Read over this thread on how to deal with ".sit" & ".bin" type files directly on Windows, prior to moving their extracted files to B2 or SS.