Is there any reason to get Link's Awakening over Link's Awakening DX?
Yes. The DX version makes several changes from the original, some of which apply to playing the DX version in B&W:
- Color (though I think some of the color choices are overly bright...)
- The okay but not amazing color-only dungeon with some somewhat overpowered tunics as a reward; this does not apply to the original version, but in color it's a change.
- More hints in dungeons. In the original version, each dungeon has one Stone Slab piece which, when collected, gives you a hint for that dungeon when you bring it to a Stone Slab. In the DX version though, the stone slabs are replaced with Owl Statues and the slab pieces with Owl Statue beaks, and there are now multiple hints per dungeon, to make things a bit easier.
- The Camera Store is added in the DX version. Here you can get a camera, and at certain points in the game you can collect photos of key scenes which you can then print out with a Game Boy Printer. The camera, pictures, and printer support work equally in B&W or color. The overworld map tile where the camera store is in the DX version is just a mountain corner or such in the original game.
- There may also be some game balance changes in the DX version?
So yeah, the original version has no photos to collect and fewer hints, for two things which also apply to B&W. I got the original version back in the early '90s though, it's the version I played. In comparison, I did not get the DX version when it came out, but only got it years later. It's great, but I have always thought that none of the DX version changes are actually essential; the original version has always been my favorite, and still is. The addition of color somehow looks a little garish at times, the added hints aren't needed, the blue or red tunics are unnecessary, and the camera stuff... it's neat I guess, but hardly something I care too much about.
No. The colorization in dual-mode carts is just pallets defined for the 4 color grayscale for each tile. It's ignored in original GameBoy.
In this case you need a GBC to enter the color dungeon, but the rest of it is the same, and you can load a save file on either platform, color or B&W. There are some game where that is not the case, though -- even though it looks the same apart for the color Wario Land II only allows one save file on the cart at a time and you cannot load a color save on an original GB and vice versa, it'll ask you to delete the file if you want to play. This is probably not the only such game.
Or for the most infamous example, Conker's Pocket Tales is a completely different game on each platform. There really are two games on that cart, a B&W one and a color one. Both are similar top-down action-adventure games, but they are definitely not the same. Again the save files are incompatible so you can't play both at once and need to delete the files to play the other version, unfortunately. I like the B&W version more, myself. The color version has a larger world and save anywhere while the B&W one has save points, but still, that one feels more fun.