For dumping DS games and dumping/restoring save files when using a slot-1 device, use Rudolph's Wifi tool. For dumping/restoring save files, you can also use SavSender. For dumping GBA games using a slot-1 device, use GBAldr by cory1492. For dumping/restoring GBA saves using a slot-2 device, use Chishm's cart_save tool. For dumping GBA saves from a slot-1 device, use EEPINATOR but keep in mind it only works with SRAM saves, not EEPROM or Flash.
Rudolph's DS Backup Tool and
usage guide
SavSender,
usage guide 1, and
usage guide 2
GBAldr
cart_save
EEPINATOR
You can't use REIN and EEPINATOR to do DS game saves because the R4 doesn't reinitialize the filesystem upon reinsertion, so it won't be able to write the save to your microSD card. That's why you must use a Wifi-based tool to do this.