I know that you can play Japanese SFC cart in an American SNES by cutting the tabs inside, but can you play them on an American SNES Jr (aka Mini) without any modification? Thanks!
No, you still need to cut the tabs off. :)
Yes, this is exactly what I did on my SNES Jr. and it works great! If you have an RGB capable TV/monitor then I recommend RGB modding the console as well. It's really easy and the picture is fantastic! :D
cant you use a RGB cord from gamecube instead?
If you mean a PAL RGB Gamecube cord, then yes (the NTSC Gamecube doesn't output RGB). If not, then no - you need a NTSC SNES RGB cord. But you'll still need to mod your console because the RGB signals aren't internally connected on a SNES Jr. It's an easy mod, though:
http://gamesx.com/wiki/doku.php?id=av:snes2rgb (http://gamesx.com/wiki/doku.php?id=av:snes2rgb)