How does a company proxy server act in reporting internet usage of employees?

"It is much more likely that the proxy server solution will enable them to determine who the usage belongs to, rather than just where it was done (eg by PC name).

Of course, this does depend on what it is and what you had before, but typically some kind of user authentication will be used (quite possibly transparent to the user). This improves non-repudiation (""it wasn't me, I left my machine on when I went out to lunch"") and enables clever rules (""let some people have this content but not you"")

Unless someone is very bored they will almost certainly never waste their time looking at full logs. More likely they will look at exception reports (attempts to access blocked sites for example), and outliers (top 20 sites, top 10 users by volume or time on line, etc).

Depending on the law of the country you are in, you may be covered by data protection and/or human rights legislation which (in the UK for example) would mean you should at least be allowed to know what data is being collected, for what purpose, how long it is kept, and be entitled to see it (your data) for yourself.
This does not stop them collecting it or using it, and asking awkward questions may call attention to yourself that you do not want, that's up to you."