"I do not like Monday!"
Translation:אני לא אוהבת את יום שני!
Is the את really necessary here? As far as I understand, we need את if we have a direct object with a definite article, that is, when we mean THE specific thing. In this case, it looks like the speaker means Monday in general, as a regularly occurring day of the week, not any specific Monday. Why את, then?
That's near true but not quite. את is required when the direct object is definite, not only when it has the definite article. For example, אני לא אוהב את דרור. There is no definite article but דרור, which is a proper name, is definite.
As to יום שני... I find that it's hard to explain. But I would say היום השני בשבוע, even though I mean the second day of each week. So it's definite. Alternatively, you could say אני לא אוהב ימי שני and it means the same thing. I can't rationalise it more than that, maybe someone else can shed more light on this.
I thought of "עבר עליי יום שני עמוס מאוד שבוע שעבר" (and not העמוס).
That said I still think "יום שני" is definite by itself, with a few exceptions. I believe it's very similar to "חודש יולי" (month of July) - what I mean is that "יום שני" is used as a name and therefore it is (mostly) treated as a definite object.