Shawn asks Hannah and Chris to be in charge of each of the committees.

"To be in charge of something" means to lead something or to have responsibility for leading a group.

As in the formal meetings, Hannah and Chris are going to be the leaders, we could call them the "chairpersons," of the committees.

Shawn says that it is important for everyone to get together, or to meet, regularly so that they can monitor the committees' progress.

"To monitor (monitor) something" means to watch something to see whether and how it changes over time.

It can mean to check on the progress of a project or something similar - "to monitor something."

Monitoring the committees' progress means knowing what the committees are doing.

While you're exercising, for example, you might monitor your heart to know how hard it is working.

Shawn says, "Let's plan on meeting once a week."

"To plan on something" means to decide to do something in the future, or to make a plan.

"Once a week" means one time per week; you could also say "weekly" (weekly), such as every Monday, every Wednesday, or every Saturday.

Shawn wants the group to meet one time per week.