According to the corebook, page 210, it states that, if exposed to flame for two rounds or is successfully hit with a Flame weapon, he MUST make an Agility test each round or catch fire. Can he do anything else that round? If not, does he continually make an Agility test every round (and nothing else) until he inevitably catches fire?

Also, if a person is on fire he must make a Willpower test to act normally. It also states that the unlucky person takes one level of Fatigue. Does his Willpower test suffer from the effects of his new Fatigue (i.e. -10)?

Thanks.

Just making the agility test does not take up his round he may act normally.

He must make an agility test every round starting on the second that he is exposed to the same fire source. Lets say a character is forced to stand in a campfire (for some reason). Starting the second round and every round thereafter that he remains in the fire he must test to see if catches on fire. If he has not cought on fire in 4 rounds and steps out of the fire he would stop making agility tests.

As per the RAW yes fatigue would effect your rolls. Notice however it specifically mentions the GM should modify those rolls based on circumstances.