I think you're mixing up some things here.
AmiKit/Winuae is an emulated Amiga. If you want you can just use it as you would normally a computer. So use a browser to download any files you want within Amikit. Just as on a PC. What you do with those files depends on what they actually are; just as on a PC. So archives (zip lha...) need to be extracted, video files played in a player, music etc...
As for adf files, they are images of floppy disks. You can mount them from within Amikit/Winuae in a virtual floppy disk (like Diskimage) or write them to floppy. Writing them to a real floppy can only be done on a real Amiga or a Catweasel card because the PC floppy drive uses a different format. Luckily Winuae offers virtual floppy drives itself. So you use an adf file in Windows and select it in the Winuae config menu in a drive. The emulation will then treat it as if it were a real floppy on the Amiga. A lot of adf files are images of floppies that are not AmigaDOS compatible. That means that they are not useable in Workbench (the OS desktop) but will work if you boot from the disk.