May one eat who avoids certain foods as a stringency (eg. foods which aren't Chalav Yisroel, Pas Yisroel, and Bishul Yisroel) use plates and/or cutlery that are otherwise kosher but have been used in the past with those foods which he avoids?
If something is not Bishul Yisroel but needs to be it is not Kosher, and Kashering is required.
I am not aware of any opinion that says that Pas Yisroel requires Kashering, even those who, based on the Arizal, are very strict about it.
Assuming the non-Cholov Yisroel here is what is popularly called "Cholov Stam" - that is standard supermarket available milk in a first world country - this is a whole discussion with various opinions. Among Chassidim who keep Cholov Yisroel they often insist on Kashering.
That being said, the tone of this question seems like you need to read this one. You are asking random people on the internet for advice you yourself are calling "VERY IMPORTANT" - think about that for a second.