If you ate some forbidden food no berachos are to be said. Not before the food nor after. You actually will be making the transgression worse. This is only when it was eaten intentionally, but if you did not know the food was forbidden or you ate it to save your life you do bless over the food. (ShA1,2 – MB3,4)
When you hear someone saying a blessing upon forbidden food, do not answer omayn. (MB2)
Someone who ate forbidden food does not combine for a zimun even if he didn’t realize it was forbidden. (ShA1 – MB4)
If two people ate meat and the third ate cheese, they can combine for a zimun. Although the two aren’t able to eat the third person’s cheese, since all the people may eat the meaty bread (the one who ate cheese just needs to wipe his mouth and rinse it out) it is considered as if they ate together. The one who had cheese should lead the zimun unless one of the others is a cohen. (MB9 – ShaH12)
If two people ate meat and the third ate hard cheese, they cannot combine. Since the custom nowadays is not to eat meat after hard cheese, they do not share common bread. (MB9)
Those who eat meat during the Nine Days cannot combine for a zimun with those who do not. (MB9)
If all three ate a k’zayis of bread before eating their meat or cheese with it – or one of the people was eating from a clean loaf which could be shared with the others, they combine for zimun. (MB9)