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If I remember correctly, that box is indeed Pokémon that were trapped when the Dream World shutdown. I had spoken with Kurt a while back about adding Misc read-only slots for HGSS Pokewalker and also Dream World Pokémon for the purposes of allowing users to recover them. HGSS Pokewalker does have an ingame recovery method (On the Pokéwalker menu, hold Down + X + L to manually retrieve your Pokémon), but that only works if you still have the game, if your savefile is orphaned from the cart then you'd be out of luck. There's no ingame recovery method for Pokémon left sleeping in the Dream World post-server shutdown, so in this case PKHeX is now the ONLY recovery method available for lost Dream World mons.

Correct, there usually is never a need to have older versions of the program. Newest is always latest & greatest. The Options -> Settings allows you to select a save file version that the program opens up with, and change the startup detection so it doesn't grab your latest savedata to auto-open. Tons of things you can tweak.

isn't misc the egg pokemon waiting at the daycare ?

Both examples shown were for Pokemon BW... In the end, I was able to fix the "bad hack" and the red square doesn't appear anymore... but that Pokemon appearing on the Misc box for the other file remains a mystery lol... could it be a Pokémon that was sent to sleep to the DreamWorld but was never woken up? lol

If I remember correctly, there are a lot more values and flags that would need to be altered to actually set your streak to a different value when you enter the tower, however the streak values recorded in your trainer card will obey whatever you set RENSHOU_SINGLE and RENSHOU_SINGLE_NOW to. Even if the tower says you're on battle 3 and battle 4 when you go to resume your streak, if you edit your streak values on the trainer card to 42 first, it should record "battle 42 and battle 43" in your streak record.

Make sure the Micro SD card is not locked to Read-only mode. There may be a small tab on the of the card that says "lock". If you are using an FTP client like Filezilla to move files without removing the SD card from the 3DS, make sure it is set to Binary mode, not ASCII mode. When exporting the save from PKHeX, you don't try to export directly to the SD card, export the file to a location on your computer, (like your desktop), THEN copy it back to your SD card. If you've done all of the above and it still corrupts, then make sure PKHeX and Checkpoint are both up to date, or try JKSM instead of Checkpoint. Keep an unedited working backup of any and all savefiles you don't want to lose.

PKHeX has the encounter database, and additionally can edit the dream world entree forest rooms too. No need for other programs.

Sorry for my late reply. If the player presses the A button in the gift screen, a HELLO message is sent immediately, acting as master. If no HELLO message is received as response, the game switches to slave mode, waiting for HELLO messages from other games for a few seconds. If no message is received during this time, IR communication is disabled until the A button to be pressed again. Thus, the player who presses the A button first will effectively start with in the slave role (since he won't receive a response on his HELLO message sent as master), while the player who presses the A button afterwards will start with the master role.