"Meine Eltern lesen beim Frühstück Zeitung."
Translation:My parents read the paper at breakfast.
It is hard to explain. It does not work with "Buch" for example. The connection between "Zeitung" and "lesen" is very strong. It seems to me that "Zeitung" starts to behave like a particle. Consider "aufräumen" (to "tidy up") -> "Er räumt auf." (He's tidying up."); "Zeitung lesen" -> "Er liest Zeitung."
"At breakfast" is the usual phrase in English (also, "at lunch," "at dinner," "at supper").
You wouldn't say "at the breakfast" in English unless you were referring to some sort of event (e.g., something to which a lot of people were invited for some ceremonial purpose). If want to say your parents come down to their kitchen in their robes and slippers, make coffee and toast, and sit down at the table with the newspaper to start the day--then you'd just say "at breakfast."
I've got so many wrong from choosing by when it should be at, and at when it should be by.
So I am to assume that beim and am are completely interchangable then or not? Because even though it's not common you could plausibly say reading the newspaper by the breakfast.
So if 'beim' isn't capable of being 'by the' as well as 'at the' then why even use beim at all over 'am' in this case?