1) (shortened) Have any of you applied for a job that requires a security clearance?
2) Has your computer lifestyle ever affected that?
1) Yes.
2) No. During the application process they did ask cyber-security related questions, but they mainly look into if you have ever abused substances/alcohol, what countries you have traveled to, and if you are a conscientious objector (i.e you knowingly oppose the government).
they could and most likely would monitor your activity
On a government network, and depending on the classification of that network (classified/unclassified), yes, but they can't monitor your activity from your home without first contacting a police/federal agency, and have probable cause that you have committed a crime.
EDIT: theellimist, feel free to PM if you have any more questions on this matter.