*.tap files don't work with SD2IEC devices. Unless you own a C64SD V2 with ITS or a C64SD Princess.
*.a0 files are raw binary files which lack the load address in the first two bytes. Directly they can only be used with VICE, on real hardware you'll have to prepend the load address beforehand. At the moment, this is beyond the scope of this troubleshooting post.
*.prg files should work straight from the host directory, also without any browser, but of course you need the necessary RAM expansion for the program that you want to run.
As a starter, take my
games collection, and unzip it into the root directory of your SD card.
At the startup prompt of the VIC-20, load the directory of the SD card with
LOAD"$",8 and confirm with a
LIST command, that the disk image "GAMES.D64" is there.
Then, change into (or better said, mount) the *.d64 file with
OPEN15,8,15,"CD:GAMES.D64":CLOSE15
Once again, check with
LOAD"$",8 and
LIST that you get the directory of the disk image. Confirm that the first file is named "BOOT".
Finally load this file with
LOAD"BOOT",8,1 - this autostarts a menu and from this point you should be able to play one of the 21 games.
If any of those steps fail, please tell what exactly goes wrong.