2XtremeENFP, re. "do you believe that different personality types handle 'addictions' in different ways? Do they manifest themselves differently?" I think one thing to note when it comes to INFJs is much of the time they are perfectionists who also want to have a high level of control over their lives and the things that happen in it. many aspects of eating disorders revolve around trying to put control back into your life when there is something going on which you cannot make better no matter how hard you try.
I have recently been reflecting on the people i have 'doorslammed,' especially one doorslam which I did to a friend who was very toxic, but not in a malicious or purposeful way. i have been wondering if i regret it and if perhaps i had been too harsh at the time (i haven't reached a conclusion about this yet, i don't 'regret' doing it in so far as it was the right thing for me to do at the time, but i am unsure if i should try to amend what i did in that i can understand how abrupt and painful it may be on the receiving side). I think it would help you to reflect on why she has shut you out of her life. doorslamming comes from a sense of betrayal and it has its roots in the INFJs morals and principles (at least, that is how I understand it). if your intentions were 'pure' (unselfish, well-intended), you have a chance to amend your relationship. although rare to amend a doorslammed relationship, a well developed INFJ should be able to see past their own limitations and consider new information or amend their beliefs with enough evidence. IINFJs will always appreciate those that put in genuine effort, but it must be genuine, and it must be worthwhile for them to accept you back into their life. this being said, doorslams are not an easy decision for INFJs to make and it is a last-resort approach, so you will need to understand what led to this happening before you can make amends.
onto your next questions - eating disorders are extremely complicated. personally, this is a topic very close to my heart. it has been 6 years since i started developing an eating disorder and it has taken me nearly that long to reach out for help.
the first thing to know is that INFJs put other people first. for me, i continually denied to myself and others that the ED even existed. i did not have time to (and indeed, in a way i did not want to) care about myself because at the time i put all my energy and emotion into helping the people around me who were at conflict. INFJ will be loathe to focus on themselves if they 'should' be helping the people they love. of course, there are a multitude of reasons EDs develop, but that is what it was for me.
i could not say if INFJs are more prone to develop EDs, but from what i've experienced, i would say that yes, given the right circumstances, INFJs are susceptible to going down that path. perfectionism, rigid principles, determination, need to have control and order in their lives - these are all things that don't mix well with stressful circumstances and conflicts in the INFJs life. being unable to make things 'better' or help others despite trying the hardest out of all involved will take a great toll on INFJ. this is where it gets complicated. EDs are an awful, consuming illness which revolves around secrecy, shame, guilt and denial. this makes it a very difficult illness to identify and approach, for both the person suffering and those around them.
it is difficult to say whether it would be better to let INFJ know that you want to help them or to try and help them without letting them know. personally, i think INFJ will feel overwhelmingly grateful if someone cared enough about them to see past how well they hide an ED to see that they are not well. INFJ wants to be open and close to people, lying and manipulating caused by the ED goes against INFJs strong principles and hurts them to have to do it. personally, i think i would feel betrayed if someone tried to help me without letting me know - if i found out later it would feel like a betrayal and it would feel more like pity than if they had told me about it first. if you genuinely care and are ready to put your emotion and time into them, INFJ will feel it.
there is no sure way to approach EDs. all i think i can really say is that if people are not ready to recover, they will not. one uniquely dangerous thing about EDs is that when you are right in the middle of it, often you do not want to 'recover.' perhaps for INFJ especially, if they are not ready to recover you won't be able to convince them to. having said this, i was very good at hiding the ED and perhaps if someone had noticed, i would have seen that i needed help earlier. i also think INFJ will recover much faster than average once they are determined to do so. INFJ is extremely passionate and decisive - when they decide to recover, they will put all their mind to it and will not give up.
do what you think is the right thing. make sure you are open and honest in your communications. figure out why you were doorslammed and be compassionate, genuine and resilient in your interactions with INFJ. one last recommendation i can make - read the book '8 Keys to Recovery from and Eating Disorder' by Carolyn Costin - this was the very first resource i read when i decided to recover and it gave me so much information that i didn't realize i needed at the time.
best of luck - you are doing a good thing when you are trying to help others - and remember that you cannot go wrong if you try to help - even if you make mistakes, you will learn from them.