If one ate a forbidden item (even it is forbidden only by the sages), one cannot make a zimun on it or say a blessing on it, neither before or after it.
If one ate a forbidden item in a place of danger, he is allowed to bless on it.
Three ate together: one of them is careful not to eat gentile made bread and the other is not careful [ie he eats gentile made bread], or one of them is a Kohane and he eats challah. Even though the one who is careful [not to eat gentile made bread] can not eat [gentile made bread] with the one who is not careful, and [even though] a Yisrael cannot [eat challah] with the Kohane, since the one who is not careful [ie he eats gentile made bread] can eat [Jewish made bread] with the one who is careful, and [since] a Kohane is permitted to eat bread with a Yisrael, [when these eat together] they combine [to form a zimun]. But when there are Kohanim and a Non-Kohane eating together and the Kohanim are eating Challah and they are careful not to eat the gentile made bread, when the Non-Kohane is eating gentile made bread, they do not combine. The same law applies when three take vows [to benefit] from each other.
A zimun cannot be made with a person that had less than a cazayit (olive's volume).