The "is to" means "is expected to" the way I read the sentence. I think that if the sentence was phrased as "he will ask" it would be more definite and by using "is to" the writer is indicating she thinks it's very likely but can't be certain that the Prime Minister will ask.
"Put" has a similar meaning as "set" in this context, but the phrase is typically "set a course" in the sense of a captain steering a ship or "put on the path" which has more of a sense of pointing a person in the correct direction and they will walk down the road themselves.
For example, "The teacher put the students on the path to enlightenment." and "The principal set the school on course to have the best math program in the country."