You know when you put a GB or GBC game on the Super Game Boy, you sometimes get a nice border.
Can this be extracted using some tool? And if so, can they be edited and re-inserted?
Is there even a tool to do that? Or at least one to look at the inside of the rom's graphics?

At least for the Pokemon games, the SGB borders are plain old 4BPP tiles like the ones used in any other SNES game. I'm not sure about other games, but I assume it's the same for them.

I'll echo what's already been said about it generally being stored as regular graphics. I recently got around to translating the Super Gameboy border for my old Ultraman Ball translation. It was stored in standard 4BPP. I had originally had trouble editing it because I was attempting to do so in the same codec as the Gameboy graphics, which didn't work out so well for obvious reasons. From my experiences hacking Survival Kids 2, I can also say that it's border was stored in the same manner.

Sort of. But there's no real Super Game Boy emulator yet.

GB/C/A emulators can only display/change a game's own borders. SNES code such as the SGB menu doesn't work.

SNES emulators can run an SGB rom, yet don't emulate the GB hardware so there's no way to "insert" a cartridge.

Multi-player would be a major barrier there. Since SGB2 has a link port. To fully support that, you'd have to emulate several SNESs and GBs at the same time...

Well, I'm not a programmer so I don't know the specifics.

I see...
So, about the games that store the borders in an uncompressed form, is there a tool that lets one extract them without having to play the game?

Some games have multiple borders (Dragon Warrior 1 & 2, Street Fighter 2) and it would be a plus to extract them without having to reach a certain point in the game to see them.

P.S.
Kit, why so mean to Rey?

What would you mean by "opcode accurate" emulator (just curious since I also tried my hand a bit at emulator programming when I was younger and even less skilled then I am today T_T I've been meaning to get back into it though)?
That it doesn't emulate a load command as a store command? Or is it somehow related to Opcode timing? When I was trying to write one myself the timing was always the most difficult thing to handle. Maybe I approached the whole thing from a wrong angle. I heard that many less accurate emulator's practically don't emulate any timing at all or only very rudimentary. Well, I have no idea how that could work since at least on the platform I was looking at a ton of I/O things were tied to timing. How to trigger everything even roughly at the right time without any timing was beyond me back then. I haven't thought about the problem in years though, so I'm curious now that someone brough up the topic ^^

Also, why do people want a SGB emulator? There is nothing to it other than the borders and maybe 2 player support in a handful of games (I had Battle Arena Toshinden for GB which worked in versus with 2 controllers on SGB). All of this could be handled in a GB emu, and most do it too (haven't looked for that 2p feature yet though).