That tool doesn't quite say that it works on slim PSPs, so I'd avoid buying it out of fear of a bad investment. I recommend you read my FAQ in the bottom of my Pandora's Battery tutorial here on PSPBrew in order to get a link for the despertar cementerio tool. Basically, it is the same thing you found there. It's a Pandora's Battery only it's custom-made for slim PSP's. What you link to won't work for a slim I don't think, and you can use the memory stick the PSP comes with for the magic memory stick. You don't need to spend money for the memory card too. Now I'll number off from here on out.
1. It would work just as all the rest regarding homebrew after you use the despertar cementerio tool for the slim (or made one yourself). If you're capable of using the tool, and it works, you're good to go. Homebrew will work if you install it correctly from that point on (although you may want to make a few changes to the custom firmware's recovery mode, but we aren't there yet).
2. You only use the tool and magic memory stick one time, and then you can format the 512mb memory stick in the PSP or Windows (or both) and you can use that for extra storage

. Also, I don't think you'll be able to turn the battery back into a normal battery if you use one of those tools, but if you can, in my tutorial for Pandora's Battery, it pretty much tells you how to make the battery normal again. Anywho, long story short, the tool won't power the PSP on... I know that sounds goofy, but it won't power it on for normal play. You'd just use the battery that the PSP comes with after you use the tool.
3. The PSP may come with a 1gb memory stick in the bundle. 1gb is a fairly sufficient amount of space, but if you want to load up the PSP with as much as you possibly can, you can purchase an 8gb memory stick pro duo. That's the largest capacity that the PSP will recognize right now (and also that is made in general). They go for about $90 or something on newegg.com I think.
4. That tool you linked to probably would stick out and "look lame", yes, but you don't keep that in the PSP. You take it out after using it for 5 or so minutes and use your normal battery that the PSP comes with. It sticks out b/c it's the size of a "fat" PSP battery as opposed to the new slim ones.
5. The original PSP menu is also left fully intact! In fact, you can even add custom themes and make your PSP a one-of-a-kind unit. The only thing that looks really "basic" and "command prompt-like" is the recovery mode in which you'll barely use in the first place.
6. Yes, it's a ton of questions, but stick around, and you'll learn this kind of sh*t

lol
7. Welcome to the forum!
*EDIT* ~ I added the link to my tutorial and a despertar cementerio tutorial in my signature just for you. You can use those as reference so that you learn how this process is done the long way, or simply just for sh*t and giggles.
-DarkPacMan77-