Agog
A seven-letter word meaning serious and eager could be "earnest".
They can be. Eager in some circumstances suggests anxious, impatient, or enthusiastic. Excited may not mean eager to do something, but for having done something.
eager, anxious, excited, enthralled, enthusiastic, avid, impatient
Keen, enthusiastic, intent, impatient, determined?
alert. avid, agog
worried or excited eager, keen, intent, yearning, impatient, itching, desirous
. having or showing keen interest or intense desire or impatient expectancy
to be eager for knowledge of or curious about something
You could say that a person who has a "continuous desire to know the why and how of things" is incessantly curious- incessant means without ceasing, continuous and curious means eager to learn, inquisitive.
anxious, keen, hungry, impatient, itching, thirsty, enthusiastic, passionate, avid, fervent
Other words to describe "unable to wait" would be impatient, eager or anxious.
eager