Extensions are just a matter of convenience.

Imagine a DS ROM as an abandoned general store in a post-apocalyptic wasteland. Sometimes you get lucky and the cans are clearly marked: you've got ham here, beans there, carrots in another, and so on. Other times you're not so lucky, and the cans all look exactly alike. They contain the same kinds of things that the marked cans have in them, but the only way to find out which ones contain what is to open 'em up and see what's in them.

Over-the-top imagery aside, the point is that those .bin files will open just fine in a graphics editor; it's just that the ones that contain graphics haven't been helpfully signposted by the game's developers. Make sure you set the codec properly; most graphics will be in 4bpp or 8bpp GBA format.

I'd recommend Tile Layer Pro or Tile Molester myself. TM is the more advanced and feature-packed of the two, but it's persnickety in some odd ways. But then, I've never touched Rom Graphix, so I don't know if it's better or worse.

It's going to appear "all weird and grayscaled" because the graphics data doesn't include color data. It's palettized. It's like a paint-by-numbers game: the graphic data indicates which colors out of the palette are supposed to be displayed, not the colors themselves. (This is where the term "palette swapping" comes from: if you want a green Mario or a Player 2 Ryu, you don't need two different sprites: just display the usual sprite with a different palette.)

There's nothing stopping you from editing the graphics anyway, but it's possible, with some work, to dump the appropriate palette using an emulator (or find it in the files you're trying to edit) and load it in your editor of choice.