Learn Hardcore Greek: Προσπαθώ να μιλήσω πιο αργά όταν σε βλέπω, επειδή καταλαβαίνεις καλύτερα. - I try to speak more slowly when I see you, because you understand better.

Προσπαθώ ends in -ώ = “I”.
καταλαβαίνεις ends in -εις = “you (singular)”. You add εγώ/εσύ only for emphasis: Εγώ προσπαθώ… επειδή εσύ καταλαβαίνεις…

Why is it να μιλήσω and not να μιλάω?

It’s aspect:

να μιλήσω (perfective) = try to carry out the act of speaking more slowly (each time, as a whole).
να μιλάω (imperfective) = try to keep speaking more slowly (emphasis on an ongoing manner). Both are possible. With a habitual time clause (όταν σε βλέπω), many speakers prefer the imperfective: Προσπαθώ να μιλάω πιο αργά…; your version focuses on the attempt at each encounter.

But μιλήσω looks like a past form. Is it past?

No. It’s the aorist stem in the subjunctive after να. Present: μιλάω/μιλώ; aorist: μίλησα; subjunctive: να μιλήσω. The aorist here encodes perfective aspect, not past time.

Why όταν σε βλέπω and not όταν σε δω?

όταν σε βλέπω (present) = whenever I see you, habitual/general time.
όταν σε δω (aorist subjunctive) = when I see you (on that particular future occasion). Your sentence is about a general habit, so the present fits.

Could I say όταν βλέπω εσένα instead of όταν σε βλέπω?

Yes, but it shifts emphasis.

σε is the unstressed object pronoun: default is όταν σε βλέπω.
εσένα is stressed for emphasis/contrast: όταν βλέπω εσένα (και όχι άλλους). You can also say όταν σε βλέπω εσένα for strong emphasis, though it’s heavier.

How would this change in the polite/plural “you”?

Use the plural forms:

όταν σας βλέπω, … επειδή καταλαβαίνετε καλύτερα. Everything else stays the same.

Is the comma before επειδή necessary?

It’s optional and stylistic. Many writers use a comma before επειδή/γιατί when adding an afterthought reason, as here. You could also write it without the comma: both are acceptable.

Can I use γιατί instead of επειδή?

Yes. γιατί also means “because” in everyday Greek: …, γιατί καταλαβαίνεις καλύτερα.

επειδή is unambiguous and a touch more neutral/formal.
γιατί can also mean “why,” but context disambiguates.

What’s the difference between πιο αργά and πιο σιγά here?

πιο αργά = more slowly (speed/tempo).
πιο σιγά = more quietly/softer (volume). With μιλήσω/μιλάω, choose based on what you mean: speed vs volume.

Could πιο αργά mean “later” instead of “more slowly”?

In time expressions, πιο αργά can mean “later,” but with a verb of speaking it’s read as manner (slowly). If you want “later” unambiguously, prefer αργότερα: Θα μιλήσουμε αργότερα.

Why καλύτερα and not πιο καλά?

Both are correct and mean “better.”

καλύτερα is the synthetic comparative of καλά and is very idiomatic.
πιο καλά is also common. No real difference in meaning here.

What’s the difference between μιλάω and μιλώ?

They’re variants of the same verb “to speak.”

μιλάω is the more colloquial full form.
μιλώ is the shorter form, often a bit more formal or written. Their aorist and subjunctive use the same stem: μίλησα, να μιλήσω.

Can I say προσπαθώ για να μιλήσω?

No. After verbs like προσπαθώ, use να: Προσπαθώ να μιλήσω… Use για να to express purpose with a different main verb: Μιλάω πιο αργά για να καταλάβεις καλύτερα (“I speak more slowly in order for you to understand better”).

Is the word order fixed? Can I start with the time or the reason?

You can reorder for emphasis:

Όταν σε βλέπω, προσπαθώ να μιλήσω πιο αργά, επειδή…
Επειδή καταλαβαίνεις καλύτερα, προσπαθώ να μιλήσω πιο αργά όταν σε βλέπω. Greek word order is flexible; commas help readability.

Where does the object pronoun go in these clauses?

Clitics like σε go before the verb of their clause:

όταν σε βλέπω With να-clauses, they go before the verb inside that clause:
Προσπαθώ να σε βοηθήσω. After imperatives, they come after the verb: Πες μου. (Not used in your sentence, but good to know.)

Is βλέπω the right verb if I mean “meet” rather than just “see”?

Colloquially, σε βλέπω can imply physically seeing/being with someone. If you want “meet” explicitly, use συναντώ/συναντάω:

Όταν σε συναντώ, προσπαθώ να μιλάω πιο αργά…