How does Freak change Maxwell from living in a "vegetative state" to taking on daily quests? What is their daily routine?

In short, Freak changes Max from being "vegetative" to being imaginative through his suggestions for quests inspired by Freak’s love of reading.  Before Freak and Max become friends, Max spends much of his time in his basement “down under” watching television.  After the two become friends (which happens when Max helps Freak get his toy down from a tree), Kevin creates many imaginative quests and shows up at Max’s house with plans already made.  This is the general “daily routine” that you mention within your question.  In fact, every morning, Freak appears under Max’s window and yells the following words:

Get outta bed, you lazy beast! There are fair maidens to rescue! Dragons to slay!

This is always the beginning of the quest for the day (which originates from Freak’s fondness for King Arthur and his knights).  One good example is the day that the two investigate a “treasure” found in the sewer. The “treasure” is actually an old purse that Freak insists belongs to a “damsel in distress.”  The two retrieve the purse using a “device” that Freak makes.  Then they deliver the purse to Loretta Lee, the owner.  Another example is the quest to escape from Blade and his gang after they bully the two boys at the fireworks show on July 4.  This is the time when Max first puts Freak on his shoulders and the two children escape together.  The next example of a quest involves going to the hospital to see the “Medical Research” unit.  Freak insists that this is where his bionic body is being created.  The final piece of evidence that Max has truly changed as a result of Freak's imagination is that Max succeeds in writing a book about their quests after recovering from the tragedy of Freak's death.