I was curious. Mozilla Firefox is not considered free software because it has some proprietary things concerning logos, correct?
Yes, it is the trademark policy that is problematic: https://lists.nongnu.org/archive/html/gnu-linux-libre/2011-08/msg00014.html https://www.mozilla.org/foundation/trademarks/policy.html Mozilla previously had non-free copyright licensing on their logos, but that was fixed a few years ago.
I would assume this was true also for Mozilla Seamonkey? I am asking because frankly I despise Firefox-type browsers. I like Seamonkey and all it has to offer, built-in e-mail for one.
Yes, I believe so: https://www.mozilla.org/foundation/trademarks/list.html
Are there any truly free alternatives to Seamonkey (if it isn't free itself)
There is Iceape on Debian, but it still /recommends/ proprietary software through the extension manager. For Trisquel, there aren't any at the moment.
Also, why does Firefox come up in the Synaptic Repository if it is not free?
It is a package which installed "Abrowser", the patched unbranded copy of Firefox with some other modifications. For example, it doesn't recommend proprietary software. Andrew.