Προλαβαίνεις να μου στείλεις μήνυμα πριν τη συνάντηση;

Προλαβαίνω literally comes from the idea of “getting ahead / getting there in time”. In everyday Greek it very often means “to have time to (do something)” or “to manage to (before a deadline)”.
So Προλαβαίνεις να…; = “Do you have time to…?” / “Can you manage to…?” (before something else happens).

Mostly time/availability. Greek uses Προλαβαίνεις; to ask whether someone can fit something in in time, not whether they are capable.
If you wanted “Are you able to?” in the skill/ability sense, you’d more likely use μπορείς.

Greek commonly uses να + verb to form a subordinate clause meaning “to do…”.
Here: Προλαβαίνεις να μου στείλεις… = “Do you have time to send me…”.

στείλεις is the aorist subjunctive form of στέλνω (to send). After να, Greek uses the subjunctive.
Aorist here doesn’t mean past; it often indicates a single, complete action: “send (one) message” (as a completed act), rather than “be sending”.

Yes, but it changes the nuance:

• να μου στείλεις μήνυμα (aorist subjunctive): “to send me a message (once)” / “shoot me a message”
• να μου στέλνεις μήνυμα (present subjunctive): suggests repeated/ongoing sending, like “to be sending me messages” or “to send me messages (regularly)”.
  In this context (before the meeting), the aorist στείλεις is the natural choice.

μου is an unstressed object pronoun meaning “to me / me”.
Greek places these short pronouns before the verb in neutral word order: να μου στείλεις = “to send me”.

Greek often omits the equivalent of “a” in casual speech when it’s understood.
So να μου στείλεις μήνυμα naturally means “send me a message” even without ένα. Adding ένα makes it slightly more explicit: να μου στείλεις ένα μήνυμα.

μήνυμα can mean “message” generally, but in modern everyday contexts it very commonly means a text/DM. If you want to specify SMS you could say sms or μήνυμα στο κινητό, but usually context covers it.

Both are correct:

• πριν τη συνάντηση is a common shorter form (especially in speech).
• πριν από τη συνάντηση is a bit more explicit/formal.
  They mean the same: “before the meeting.”

Yes. τη is the accusative feminine singular form of the definite article η (the).
συνάντηση is feminine, and after πριν it goes in the accusative: πριν τη συνάντηση.

It can be both. συνάντηση is general: any meeting/appointment/get-together. Context decides whether it’s a work meeting or a personal one.

It’s neutral to casual, because it uses 2nd person singular (Προλαβαίνεις). It’s appropriate for friends, colleagues you’re on first-name terms with, etc.
To be more formal/polite, you’d use 2nd person plural:

• Προλαβαίνετε να μου στείλετε μήνυμα πριν τη συνάντηση;

Common natural answers:

• Ναι, προλαβαίνω. = “Yes, I’ll have time.”
• Ναι, θα σου στείλω. = “Yes, I’ll send you (a message).”
• Όχι, δεν προλαβαίνω. = “No, I won’t have time.”
• Δύσκολα, δεν νομίζω να προλάβω. = “Probably not / I don’t think I’ll make it in time.”

Greek doesn’t need θα here because Προλαβαίνεις να…; already frames the situation as “Will you have time (to do it) before then?” It’s about feasibility within a time window.
You can add future in some contexts, but it’s not necessary and often sounds less natural here.