I've been trying to find information about how to put homebrew on my DS (DS roms to be exact and maybe some music) but there's a few things that are still confusing so I'd really appreciate it if someone could answer these questions:
1- Does it matter if my computer is a Mac? Will I have compability issues etc
2- Do I get any MicroSD card like a Sandisk (I've seen a few at like 10$ on ebay so...)
3- I just put the R4 card in the microSD card?
4- Do I need additionnal hardware/software to connect the microSD to my mac?
5- Is all of this compatible with a fat DS?
6- in general how big are DS games and do they work properly?

Thanks in advance, if I find any other questions I'll ask them. I'm really skeptic before buying the R4 cards and all that jazz

I can answer a few of your questions.

1 - No, that won't matter as you don't need to run any programs on your computer.  All you'll need is USB.
2 - Any brand of microSD should work but I've heard that certain cards don't like cheaper brands.  I have this card and a cheap microSD and it's working fine.
3 - There'll be a little slot at the back of your card that the microSD will fit in to.
4 - The card that you get *should* come with a little usb adapter that has usb on one end and a slot for your microSD on the other end.  The Cyclo Evolution I bought came with an adapter.
5 - Double check the info for the card you're getting but I'm almost positive that all cards work with fat DSs
6 - DS games vary in size but are usually around 30-60mb.  Some are as small as 10mb and some are over 100mb.  When I first got my microSD I put 18 games on it and they took up 1.08gb of space.  I have yet to run into a game that doesn't work properly on my DS. 

You buy the R4, and a microSD. Any microSD should work, but some are better than others for sure. You put the microSD in a usb converter that comes with the R4, then put it in your computer (I don't know about your mac issue, but it should work still I would imagine). You download the games or music, put it on the usb, take out the usb, stick the microSD into the R4, put R4 in DS, or DS lite, both work just fine. Then you load the games off the R4. The R4 itself is basically game, with external memory. From the R4 menu it just loads the roms. Smallest game is 8 megs, largest game is 128 megs. Games by default usually come multiples or whatever, as in 8, 16, 32, 64, 128. Off of the R4 website you can download a rom trimmer which makes them smaller.

DS homebrew is really awesome. The only thing that doesn't work for me SOMETIMES is download play on some games. It just doesn't work, but apparently that all depends on the quality of the card. I've never had an issue with online play or multicard play, with either Japanese or English games.

so basically I would need the R4, the Cyclo Evolution + a MicroSD card? Man that's getting expensive hahaha

EDIT: nevermind.... but is the R4 better than the Cyclo or vice-versa?
EDIT 2: I now have a Sandisk 2gb MicroSD, that one is compatible with the Cyclo right? It says it is for the 8gb but for the 2gb I can't find any info.

Yeah that's what I found. I got a 2gb Sandisk for 17$ and I'm going to order the Cyclo Evolution Black as soon as the company answers me about where their pick-up location is in Montreal.