1) Yes. Reporting is all automated. The airlines notify the US government when the person left the country, which is then matched against the record created when they entered and passed through immigration.
2) Your friend is no longer eligible to use the Visa Waiver Program. One of the conditions of the VWP is that you must have "complied with all conditions of any previous admission under the Visa Waiver Program", which your friend has not done.
In order to enter the US your friend will need to obtain a Visa. Normally an overstay on a previous visa would make obtaining a visa difficult, however I would expect that a 2 day overstay would likely not be considered serious enough to deny a visa application - although at the end of the day it's completely at the discretion of the official carrying out the visa interview.
The good news is that short overstays do not trigger any mandatory baring from the US. If your friend had overstayed more than 180 days, they would have been automatically bared from entering the US for 3 years. Over 1 year, and the bar is for 10 years.