"To draw to a close" means to be ending or finishing something.
You might feel sad when your vacation draws to a close, for example.Our "Business Meeting" course is drawing to a close because we are already in the ninth lesson and there's only one more left.
Shawn can't take any more questions because their time together drawing to a close, or ending.Shawn says that he has been very favorably impressed by today's discussion.
The expression "favorably impressed" (impressed) means having a positive opinion of something, or a feeling of admiration or respect for something.In other words, he liked the discussion and is pleased with it.
We always hope that our bosses are favorably impressed with our work, meaning they like it.Shawn says that "a great deal of work remains to be done."
A "great deal" means much, a large part, or a large portion of something, so a great deal of work means a lot of work.You might own, for example, a great deal of land - you would have a lot of land.
"To remain" (remain) means to be present, or to not be gone or finished yet.You might, for example, remain at the office until 8:00 if there's a lot of work to do - you will stay at the office until 8:00 p.m.
When Shawn says that "a great deal of work remains to be done," he means there is still a lot of work to do and they haven't finished working on these problems.