The expression "to be charged with something," here, means to be given responsibility for something, to be told to lead something, or be placed in control of something.
"To be charged with" has other meanings as well: it's often used in a legal sense.When you commit a crime - when you do something wrong - and the police catch you, they can "charge" you with a crime - they can accuse you of doing something wrong.
Here, however, "to be charged with" means to be given the responsibility to do.So, Hannah's committee is responsible for developing a new marketing campaign.
Next Shawn asks Chris to be the chairperson of the second committee.A "chairperson" is a person who heads or leads the committee.
So the leader of the committee is usually called a "chairperson."It could be a "chairman" for a man, or a "chairwoman" for a woman; a more general term is "chairperson" (all one word - chairperson).
The word "chairperson" has become more common in American businesses to refer to both men and women.Shawn says that Chris's committee will begin making the proposed product changes ASAP.
"ASAP" (all capital letters) is an abbreviation for "as soon as possible" and means, here, without delay or right away.If someone says he needs something ASAP, he means he needs it immediately - right away.
Shawn, here, is saying that Chris's committee should start making the changes on the product as soon and as quickly as it can.