INTP = Ti + Ne + Si + Fe
Do all INTP's have this exact same formula, in this exact same order?
As Magic says (and you respond), no, not in practice. This is why there are often arguments on INTPc for example on who the "real INTPs" are... or MGB's posts there (I think) that describe 6 potential different types of INTPs, and so on.
As minor points of comparison, my Ni actually ranks #3 in my function order, and has at times drifted into the top 2, although best fit was still INTP. Someone like Rajah, however, I think scores a high Te... and so we look different.
There are also INTPs who have developed their Ne and tend to use it (as part of their socializing process) much more than they outwardly use their Ti.
But you get the point. There might still be a general internal Ti thinking process, buttressed by possibilities (Ne) as a fuel for the Ti, but it's flavored heavily by whatever other functions actually are stronger in that person.
and if so, "Fe" seems the exact opposite; do all INTP's have Fe and if so, can you re-explain how Fe works with being an INTP - which seems entirely conflicting.
Not sure what you mean by the latter.
Fe is the "vent system" for INTPs, usually. It's the opposite of their primary so they tend to not feel comfortable with it naturally... and when they are under lots of pressure and their primary is not solving the problem and Ne can't get them out of it either, they tend to "flip out" emotionally, respond aggressively to perceived social pressures that might not actually exist, get hypersensitive, and so on.
INTPs can learn to use Fe just like anyone else can; it's essentially a social language one uses to prioritize and express one's commitments to others and place in the community. And since it's externalized, it doesn't run interference against the internal judging Ti process. I think this is one way in which INTPs don't instinctively "get it" -- they see Fe as an imposition by unfair/illogical social forces (because sometimes it can be leveraged as such) rather than as a voluntary means of expression that is more proactive in nature.
People like ExFJ who have Fe as a primary look different with it as their main; it's their instinctive approach, buttressed by other functions, and they tend to have developed the nuances of it.
Also, am an IxTJ. I constantly debate the N/S. How would using the functions help out?
If you are IxTJ and are sure on that, your function order is theoretically either:
ISTJ = Si + Te + Fi + Ne
INTJ = Ni + Te + Fi + Se
ISTJs think inside the box based on their understanding of how things worked and what they have experienced. (They make good engineers... they go by the book, they know what has worked and what has not, they are good at risk managing in THAT sense.... but they hesitate to go outside the "prudent".) With Ne as the inferior, they sometimes get paranoid about the possible dangers of a situation, they misjudge people and situations, they are very uncomfortable in new situations and keep trying to force it to work according to the old rules.
INTJs think outside the box and spin things around on their head. They are not nearly bound by past experience and established methods. They are good risk managers, but also tend to know when to take a risk and like to exert control with Te over the situation to circumvent the risk. With Se as the inferior, they often neglect their own bodies, they ignore external data in favor of the "way it's supposed to work!" according to their theories/ideals, they often get very internalized and just do not accept external limitations in the way ISTJs do.