Running a fully free Gentoo system is relatively simple, but whether or not you'll notice a performance hit depends on how well your hardware is supported without blobs like z3bra said. For me the main hit was my GPU, I could only use the vesa driver IIRC. If you can run a completely free system without any major performance hit I don't see why you wouldn't.

To build a fully free Gentoo system you'll need to add ACCEPT_LICENSE="-* @FREE" to your make.conf, you may also want to add USE="bindist". You'll also need to either patch whichever kernel your using (the patches and instructions are here: https://www.fsfla.org/ikiwiki/selibre/linux-libre/) or use the ck-sources with the deblob USE flag set. There used to be hardened-sources which also had the deblob USE flag but support has been dropped AFAIK.

There's a disclaimer on the Gentoo wiki license group page that says:
We are programmers, not lawyers. Our evaluation if a particular license is a free software license is only a guideline for Gentoo developers and users. It is not a legal statement. There is also no guarantee that a particular LICENSE variable in an ebuild reflects reality. So don‘t rely on it, but check the license that is included with the package itself.

In regards to your BIOS and CPU not being 100% free, if this is something you really care about take steps in that direction or maybe purchase parts that are free when you can afford to. Don't get discouraged because you can't have it all right away, do the best you can with what you have.

I wouldn't recommend switching to Gentoo for an educational experience. I'd say start with Slackware and then move to CRUX when you understand how to configure a kernel. The Gentoo wiki is great for learning how to configure and compile a kernel.

Pretty much any distro can be turned completely free, some are harder than others. If your goal is to have a completely free system start with one that is. I'd probably recommend Parabola seeing as your coming from Arch, or Debian because if your hardware isn't supported without firmware you can easily salvage the install. If I were you and had a thinkpad I'd run OpenBSD.