What are conflicts that Montag faced involving man vs. man, man vs. self, and man vs. nature?
The conflict is the struggle in the story that characters must deal with. You've named three of them; the other two are man vs. society and man vs. the unknown.
Man vs. man is most obviously seen with Montag, the protagonist, and Beatty, his boss. Beatty believes burning books is necessary because they are worthless. Montag has to kill Beatty.
Man vs. self is again seen in Montag's internal struggle when he questions his role of burning books. He starts to read books and becomes friends with Faber. He has to decide to change what he's believed all his life.
Man vs. society is can be seen when Montag begins to question the values of the society he lives in. When he has doubts, that society then turns on him, and he has to seek refuge with the book people.
Man vs. the unknown is shown by the fear of Montag's society to allow people to read books that will make them think and question established rules and traditions. Knowledge is power, and the leaders of society are afraid for power to possess this power. They are supposed to accept things as they are.
If you go to the link below, you can find other examples of these same conflicts. Always ask yourself when determining conflict what is the problem in the story or who causes what problems.