"My friend is working at a clock company."
"A good rule of thumb is that while both particles can mark the location where a verb occurs, で de tends to be used when the verb is an action, and に ni tends to be used when the verb has more to do with just being or existing."
The site also gives the examples of「います」and 「すみます」as being verbs associated with a state of existing/being (the former literally being the verb for existing). I'm guessing in Japanese「つとめる」is considered more a state of "being", rather than an action.
So, he finally got a job. It's about time! What I wonder, though, is...does he get paid by the hour? I tried calling to ask, but he was on the clock. You know, from what I heard, about half the time, the company is short-handed. However, the boss, (who is the face of the company) is good at keeping everything running like clockwork so that there's no cause for alarm.
In a very specific weird context probably could, but normally it just sounds more like a clock belonging to a company
時計の会社 [clock's company / company of clocks / company (of the clock-group)]
会社の時計 [company's clock / clock of company / clock (of the company-group)]
仲間 is more like "companion". You are two people in a similar situation/struggle with similar goals. Your coworkers and classmates can be 仲間, but it doesn't necessarily make them your friend. It's more like "we're in the same boat".
友達 is a more personal "friend", someone you may not have much in common with but someone you enjoy spending time with and can rely on.