Just to double confirm this but, I made an account just to ask this question, since the homebrew website has nothing on this.
My 3DS is the old 3DS, 1st generation model. I updated it to the latest firmware, v10.6 or whatever, the latest official firmware to this date. I also have a digital download copy of fire emblem fates: conquest, but with the birthright DLC attached onto it.
Now my question is, can I still install homebrew onto my 3DS? And if I can, can I patch the game rom?