You need to install CFW to the N2DS first of all, which I didn't see mentioned here. That's the FIRST thing you should've mentioned. Otherwise any non-legit content won't transfer.
Your question was completely clear, don't worry.
To clarify, DS mode is always enabled in AK2i. DS mode will be blocked by the console if you don't disable the blacklist via patch or CFW on FW versions >4.3 .
NTRboot always works after flashing it, regardless of the console version, because...
Flash NTRboot to AK2i. Use AK2i from CFW'd console via Home Menu. That's all! You can insert the cart in another console to use NTRboot without losing DS functionality.
Bonus: NTRboot removes that awful horse logo the cart has as a header, and replaces it with a beautiful ak2 logo.
Because the B9S bootloader should be as easy as it can be to avoid bricks. That means nothing like graphic menus, nor config parsing. Just a haxsigned code jump to a fixed location in the SD.
Is the NTRboot cart working correctly?
Insert modified cart, put the magnet in place, push the button combo, push the power button (several seconds). Remove the magnet. That should work if NTRboot is well installed into the cart.