So, I have not yet purchased BG2, but I do plan on doing so. I only have a few questions, and to make this easier, I'll number them. If you know the answer to a question, put the corresponding number next to your answer.

1. Do I need a CD key or does it come with one?

2. Will it work just fine natively with Windows 7. I tried to use my original disc's for BG1 and had sooo much trouble that I just gave up.

3. Can multiplayer be done over the internet?

4. If I buy this game, can I let my brother use my copy too? If so, can we play multiplayer with the same copy?

5. I have played this game once, it was a very long time ago, I'd like to enjoy it as it was, are there any packs/mods that I NEED to play with, or any mods that ONLY make it better. I do not want content packs (unless of course it includes more vintage-like faces) [Like the Morrowind high res mod that strictly makes the game look better]

1. No, you don't need a CD key.

2. Yes. I have Windows 7 64bit and it plays just fine.

3. Yes, via private servers -- the 'official' servers are all defunct.

4. Yes. There is no DRM with GOG games. Some, like NWN, need CD keys (for multiplayer only), which GOG provides, but BG2 doesn't need them.

5. There are no mods that you need, but mods to consider given your prerequisites are:
Ascension
Turnabout
BG2 Fixpack
Unfinished Business

Remember that 'making it better' is purely subjective, so you're likely to get people telling you to install (or don't install) X or Y mod on their preference. Make your own mind up... make the game yours, not somebody else's.

For 1-4 see Hickory's asnwers.
For 5 I disgree with Ascension and Turnabout. Both these mods mostly change things in final battle of Throne of Bhaal and certainly are not something that you need. Ascension makes it quite harder.
For needed mods you should check this stickied thread, Baldur's Gate 2 essential mods. The part 2 of first post shows what mods should be installed to make polish the game and squish most bugs. Everything else is quite optional and depends on player's preferences.

When running Vista or Windows 7, you can avoid a lot of problems by *NOT* installing older games in "C:\Program Files" or "C:\Program Files (x86)". These folders are protected against modification by Windows Vista and 7, to some extent. The game may not be able to save games because the UAC-protection prevents it. (Unless you mess with the access rights on the folders.)

Just create a seperate folder for games, such as "C:\Games", and install the (older) games into that. It will save you a lot of troubles while playing. I have many old GOG games running on Windows 7 x64, without any problems.

4. You can but the honor system requests that you don't. It has been noted in the past to treat the GOG games like books if you lend it to a friend you can't read it in the meantime until they give it back. So if your brother's playing it you should not unless you have two copies. If you had the original CD's you would not be able to because it requires a CD in the drive.

You can do whatever you want with the games you purchase that's the great thing about DRM-Free games. But just think, if you play with two people off the same download you are giving justification to all the DRM crap we get from mainstream publishers. GOG give you a choice, the mainstream publishers want to take away your right to chose because they don't think you will make the choice they want you to make.

Something to think about.

For 1-3, Hickory is correct.

For 4, you can, but whether you should is up to you. Being DRM-free you can do whatever you want with any game you buy here, including copying it 10 times and giving a copy to each of your friends.
Just remember that if everyone did that, GOG would likely go out of business.

For 5, you don't really need any mods, but the BG2 Fixpack is strongly recommended. It gets rid of almost all the bugs and makes playthroughs less frustrating.

For convenience, you might want to try the BG2 Tweakpack, it doesn't affect game content, but it can be used to change some things you find annoying (mostly making inventory management much easier). It's also modualr, so you can choose to only install the tweaks you want.
For graphics, you might want things like the widescreen mod that lets you play at higher resolutions or 1pp, which gives you better-looking icons and models for some things.

I strongly disagree with Hickory about Ascencion and Turnabout. Not only do those mods change a lot of content in ToB, it also makes that part of the game noticeably harder.
Even Unfinished Business only adds content, even if it's just things that were cut out of the final game by the devs.