1. (Rabbi Eliezer Chryser) It depends on how one defines Shogeg and Ones. "Ones" presumably refers to one who does an act with no intention to do that act. If he intends to do what he is doing but he does not know that what he is doing is forbidden, then it falls under the category of "Shogeg."

(Rabbi Yaakov Montrose) With all due respect to Rabbi Chrysler, I do not believe that "Ones" has to be that one does an act with no intent to do that act. For example, a person who is made to eat unkosher food at gunpoint is certainly called an "Ones," even though he fully intends to eat that food.

The Avodah Berurah on Horayos (pg. 71) has a large article on this very question. One answer he quotes (based on Rashi in Yevamos 87b, DH "Shelo") from the Sefer Yisron ha'Or is that Beis Din did not tell this person that he had to eat Chelev. Rather, they told him that it was permissible to eat this Chelev.

I would add to this that the person probably knew before this ruling that this Chelev had always been deemed forbidden. Being that he did not have to eat this newly permitted item, he is not called an "Ones" which is someone who is a victim of forced circumstances. This fits the criteria of a Shogeg which is acting somewhat carelessly. (See Avodah Berurah quoted above for more answers.)

2. I am not so learned in the esoteric areas of Torah, but based on logic I would assume that eating Chelev even under those circumstances does result in some form of Timtum ha'Lev.

3. Again, based on logic, I would think that just as bringing a Chatas rectifies and "undoes" and the sin, so does it "undo" the Timtum ha'Lev.

Kol Tuv,

Eliezer Chrysler and Yaakov Montrose