I'd broadly agree with you in terms of focus/tone - i.e. I think it should be aimed at newcomers, and try to convey both some of the lore and some of the functional differences/themes of the factions in terms of units/gameplay, but without being too wordy. Due to being aimed at newcomers, my preference would be to avoid references that would seem strange to non-FAFers (such as references to flying donuts and chickens).
If 1 word faction words are used I'd prefer keeping the Unite/Liberate/Cleanse words to align with the original Supcom faction art (https://www.deviantart.com/generalyin/art/SupCom-Three-Factions-50914447)
In terms of the suggestions other than my own for the actual text, I'd be happy with your suggested wording in terms of length and content (my only comment being the '1-word' start of each bullet per above); For Magge's I'd favour a slightly streamlined version of the current text so it's a bit shorter.