And now I don't know:
1) What kind of Windows Pro SP3 CD do I have to get and how? Is it OEM, Retail or something else?
You want the OEM one.
2) How can you get the .iso file of this disc? As far as I understand there is an .iso on the Microsofts TechNet, but I am not registered there. Do I have to call them?
In situations like this, I've always had an install CD handy, or known someone I could borrow one from (to rip my own ISO). I've never tried to get the ISO direct from Microsoft.
3) What will happen with the activation, will it just activate when I click ok, or does it skip activation because it's an OEM Laptop?
I believe it will try to activate just like a generic OEM install.
4) What about nLite? Is it worth customizing the install? I took a quick peek at the software, and somehow it seemed that it might cause a lot of troubles if I customize something wrong.
Unless you need third party disk controller drivers, or are starting from a pre-SP3 ISO (and want to slipstream SP3 instead of downloading and installing it separately), I don't see any real need for nLite.
5) Any other tips?
Depending on the graphics adapter in that laptop, there is a slight risk that you will have trouble finding video card drivers for it. I ran into this once a couple of years ago, with an HP laptop that had an nVidia mobile GPU. The generic drivers from nVidia's site would not recognize the GPU, and would not install. I ended up having to use some "hacked" drivers from a third-party site.
If the world isn't making sense to you, you're either drinking too much or not drinking enough.