Your Te and Fi descriptions were pretty good, but you described Fe as a sort of random, aimless "let's just have fun!" kind of function when that's really much more applicable to Se/Ne.
Fe aims to foster emotional connections between people for the purpose of organizing others into purposeful goals. Fe users do tend to make an effort to be personally and emotionally involved with others, but it's less because "hey this is FUN!" (you see that in EFPs a whole lot) and more because they feel it's their moral duty to actively make plans to help others.
As for Ti, it will solve puzzles and such for fun, yes, but I find that this is much more common for NTPs than STPs, because Ne plays a big role in the desire to complete hypothetical patterns. STPs seem to enjoy more hands-on, physical puzzles like electronics or cars, etc.
Remember that Fe is the dominant function of EFJs, meaning people who place it as one of the top two functions are going to be less sporadic/random and much more focused on external world organization.
Thank you, that was interesting. I'm not entirely surprised that I understand Te-Fi best, seeing as they are my own functions.
I think it is worth remembering that functions rairly act on there own. Your description of STPs makes complete sense to me, as it is their Se function that provides the information that the Ti function uses, so they are liable to focus in on
physical logical systems systems, such as the electronics you mentioned. NTPs gather through Ne, and so like abstraction.
I guess that idea also applies to the main question of Fi and Fe. I think the results are liable to be influenced by the percieving function used in conjunction. The descriptions of Fi/Fe I've seen above certainly seem to work when Si is used, but I'm not sure about other combinations.
I'm an Fi user myself, but I focus it through Ni, which is probably why I see most moral problems in shades of grey. Many of them probably have no answer, as the information required cannot be known. Is a war justified? Will it do more harm than good? Maybe, but it is impossible to know before hand. You just have to make a judegment call and hope you are right. I'd be inclined to say that the decision either way only becomes immoral if your reasons are not based around that judegment, such as cowardice or greed. In short it's not the actions that dictate morality but rather the intentions.
How would an Se or Ne user react? Would the Se user weigh physical suffering/distruction more prominantly than a metaphysical loss of pride or soveriegnty? Would they care much who the king is as long as they keep order and let them live their lives? And an Ne user? I'm sure yu could answer that question better than me.