Yes, I do think the government monitors our online activities, to some extent. It would not be possible for them to monitor every person's every move, but I think they use key words and key websites to track activity that might be harmful to our country. For example, the government may have alerts that are activated when someone searches for a topic that might be related or linked to international terrorist groups.
They also might monitor those who frequently visit potentially dangerous websites, such as those associated with criminal activity. I do not think that the government monitors how many times a person purchases new shirts from Amazon however. That would be way too much data to be useful.