So Τα is the article "the" in plural form, is that what is happening here?
Specifically the neuter article in the plural form, yes. (Masculine and Feminine articles have their own plural forms, like e.g. Spanish but unlike e.g. German.)
So we've been seeing διαβαζώ as "to read" and in this sentence it's translated as "to study". Is that always the case or is it just like saying "reading up for the exam"?
The dictionary will show you three words for study. μελετώ, μελετάω as we use study in "to make an effort to learn something.", σπουδάζω is used for a student in an institute of higher learning...University. etc.
However, you will most often hear, Το παιδί διαβάζει." which means "The child is studying (or the child studies)." or something like: "Έχω να διαβάζω." I have to study. or even I have homework.
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If you read the other comments on this page you'll see that both Simple Present and Presence progressive (continuous) are correct and accepted. Greek does not have separate tenses to show these. And please make a habit of reading the comments they can be really helpful.
Why not? That is the tense we use in English for something that is happening right now.
You may not need this info by now as you posted 7 months ago and you are probably understanding the tenses by now. But for anyone else who is unsure. Simple present can be either I read/am reading = διαβάζω, Simple past διάβασα = I read, Imperfect past διάβαζα = I was reading, Simple future θα διαβάσω = I will read.
Why παιδια and άντρες ? Why is άντρες not applicable in the sentence?