Learn Hardcore Greek: Αυτή φτάνει συχνά νωρίς, αλλά σήμερα άργησε. - She often arrives early, but today she was late.

Yes, Greek usually drops subject pronouns because the verb ending shows person/number. Here, Αυτή is included for emphasis or contrast (roughly “SHE is the one who often arrives early…”). A perfectly natural version is: Φτάνει συχνά νωρίς, αλλά σήμερα άργησε. You’d include Αυτή to disambiguate or stress the subject.

Why is φτάνει in the present but άργησε in the past?

φτάνει (3rd sg present) expresses a general/habitual action: “she often arrives.”
άργησε (3rd sg aorist) marks a single, completed event: “but today she was late (once).” This present-for-habit + aorist-for-one-time contrast is very typical in Greek.

Could I say έφτασε αργά instead of άργησε?

Yes, both are fine but slightly different:

άργησε = “she was late” (relative to an expected time).
έφτασε αργά = “she arrived late/late in the day” (focus on time of arrival). Your sentence could be: Αυτή φτάνει συχνά νωρίς, αλλά σήμερα έφτασε αργά. Using άργησε keeps the explicit idea of being late.

Where do the adverbs συχνά and νωρίς go? Is the order flexible?