Well, I would say that the first few parts sound like more like Fi to me, but I think we need an INFP to tell us more. I think that last one might be more related to inferior Se under stress, though.
I'm probably much weaker on functional analysis than many here. But that never stops me from giving my opinion.
I tend to think that the Dominant and Auxiliary functions are the main players, and the rest are all kind of a haze that are at various stages of development or non-development. The Tertiary function in particular comes out and becomes a big player at times of stress or conflict; for example the Joe Butts definitions of tertiary Ti and Fi that are cited in ?'s post strike me as use of Ti and Fi under stress and conflict. But otherwise, the
unstressed use of the Tertiary function remains as hazy and negligible as the other lower functions. Thus I would class the Tertiary function as just one more of the generally hazy non-playing functions (on a daily
unstressed basis).
As a result, I tend to think that all our normal, unstressed reactions to things come largely from our Dominant and Auxiliary functions. Input from lower-level functions comes largely in the form of good habits we've developed (for example, cultivating habits of Fe social politeness) or specific talents we've developed (for example, deliberately developed Si data-gathering skills).
I have always been a little confused between Ti and Fi behavior in some circumstances.
For example, what you describe is something I feel too -- but to me it tends to be intellectualized. I see it merely as a matter of consistency and logic, that things have to be uniform and coherent... including my character. I remember when I was a teenager and just thought Fe stuff was completely stupid, even though I did not want to stir up trouble; to me, it was inconsistent to show one thing but believe another inside, and I hated it.
So it seems to me that either Fi is much broader in scope, or that Ti can mimic Fi, just in more impersonal ways. But how can I compare my subjective internal experience to yours, and thus determine that yours was more personal/Fi and mine was more impersonal/Ti? I don't know the answer to that.
In this case, I would say that
all people have a visceral reaction to the contrast between sincerity and insincerity, the same way that all people have a visceral reaction to the contrast between love and hate or the contrast between acceptance and rejection. Those things get drilled into us in early childhood as part of routine socialization, probably even before most of the individual MBTI functions develop. The only difference is how the individual chooses to express that reaction as adults. For example, an INFP will react to insincerity via Fi, while the INTP will react to insincerity via Ti. That is, presumably the underlying visceral reaction is the same in both cases, but the INFP will choose to express his reaction in emotional terms whereas the INTP disregards the emotional channel and evaluates and expresses via an intellectual channel.
INxJs might be a slightly different case. The dominant function for INTPs and INFPs is a Judging function, whereas the dominant function for INxJs is a Perceiving function (Ni). If INxJs have a strong reaction to insincerity on the level of a "Judgment," then it may indicate that they are reacting to the insincerity via their Auxiliary (Judging) function (Fe in INFJs and Te in INTJs). For example, in their dealings with other people, if they spot insincerity in another person they react with an instant dislike for that person. (Meanwhile their Perceiving Ni might see insincerity as just a factor to be evaluated in internal evaluations.) But that is speculation on my part, since I'm not an INxJ.
Getting back to the Tertiary function: I would write off the Tertiary function as a contributor to feelings about insincerity (except under conditions of conflict and stress). I don't think people need to go searching out Fi in oneself in the lower functions in order to dislike insincerity. All of us, regardless of type, seem to be able to recognize right vs. wrong and even react strongly to it, as a result of basic socialization when we are growing up. IMO, our functions don't have anything to do with
recognizing right vs. wrong; instead, they only reflect how we
react to right vs. wrong. And a good interaction between the Dominant and Auxiliary functions will give us all the tools we need for that. IOW, there's no particular reason to delve past our Dominant and Auxiliary functions except where specific skills are demanded by the environment or we desire to develop those skills ourselves.
To expand on that last point: For most cases, it seems to me that a good interaction between the Dominant and Auxiliary functions will 1) give all of us adequate doorways to both the inner and outer worlds; 2) give all of us both a Judging function and a Perceiving function with which to carry out the full cycle of evaluation and decision; 3) and as a result, give all of us a couple different ways (J and P) to react to and express the internalized, universal evaluations of right and wrong that were drilled into us as a result of basic socialization when we are growing up. After all that, skills coming from the lower functions are just icing on the cake--they are supplementary tools that we can develop or not, depending on our environment and personal needs.
Don't ask me to prove all this; I can't. I'm just kind of throwing this out as anecdotal experience. (Athenian200 asked for INFP input on Fi, and I got thinking about it.) This is just my own evaluation of how I myself use my Dominant and Auxiliary functions, as opposed to how I've developed individual skills from my lower functions. And my Tertiary function (Si in INFPs) seems to fall in with the lower functions, in that the
unstressed use of the Tertiary function is simply one more skill to be developed, and then turned on and off as needed. (In practice, I certainly don't see Si data-gathering as part of my natural, visceral reaction to anything except stress and conflict.)