The government doesn’t need to look for those documents. They already have them!!
Naive. First, you are assuming that the docs may be valid. You also forgot.. it was a Pakistani passport, not a US passport. The passport will contain stamps from other countries visited. This info is not necessarily recorded on entry into the US. To get the academic records, the authorities have to know which universities attended and then has to get a warrant or subpoena for the records.
The greeting cards would show who he might be associated with/lines of communication. Last time I checked, our mail is not monitored.
Don’t forget, this guy was on the no-fly-list.. how many times did he take a flight while on that list? When they caught him, they pulled him off of a flight that had already pushed off from the terminal.