Learn Hardcore Greek: Αν θέλεις βοήθεια με τα ελληνικά, βεβαίως μπορώ να σου στείλω μερικές ασκήσεις. - If you want help with Greek, of course I can send you some exercises.

Here, βοήθεια is a noun (help, the thing), so you don’t use να.
Αν θέλεις βοήθεια literally means If you want help (not if you want to help).

What is βοήθεια exactly – a noun or a verb? How would I say to help?

Βοήθεια is a noun meaning help, assistance.

Θέλω βοήθεια. = I want help.
Χρειάζομαι βοήθεια. = I need help.

The verb to help is βοηθάω (more colloquial) or βοηθώ (slightly more formal).

Examples:

Θέλω να σε βοηθήσω. = I want to help you.
Με βοήθησες πολύ. = You helped me a lot.

Why is it με τα ελληνικά and not στα ελληνικά? What’s the difference?

Both με τα ελληνικά and στα ελληνικά are correct but mean different things:

με τα ελληνικά = with Greek (as a subject / skill)
- χρειάζομαι βοήθεια με τα ελληνικά = I need help with Greek (learning the language)
στα ελληνικά = in Greek (as a language of communication)
- Μπορείς να το γράψεις στα ελληνικά; = Can you write it in Greek?

In your sentence, the meaning is help with (learning/using) Greek, so με τα ελληνικά is the right choice.

Why do we say τα ελληνικά and not just ελληνικά?

For languages, Greek usually uses the definite article:

τα ελληνικά = Greek (language)
τα αγγλικά = English
τα γαλλικά = French

Grammar notes:

ελληνικά is the neuter plural form of the adjective ελληνικός (Greek).
With the article τα, it functions as a noun: the Greek (language).

So τα ελληνικά literally is the Greek (language).

What does βεβαίως mean, and how is it different from βέβαια or φυσικά?

Βεβαίως means of course, certainly, sure.

Common alternatives:

βέβαια
φυσικά

In this sentence, you could say:

…βεβαίως μπορώ…
…βέβαια μπορώ…
…φυσικά μπορώ…

All three are natural; βεβαίως can sound a touch more formal or polite, βέβαια and φυσικά a bit more casual, but the difference is small in everyday speech.

Why is the word order βεβαίως μπορώ and not μπορώ βεβαίως?

Both orders are possible:

Βεβαίως μπορώ να σου στείλω… = Of course I can send you…
Μπορώ, βεβαίως, να σου στείλω… = I can, of course, send you…

Placing βεβαίως at the beginning sounds very natural and emphasizes the of course.
Placing it after μπορώ emphasizes the can a little more. Word order in Greek is flexible; the choice mainly affects emphasis and rhythm, not grammar correctness.

What does σου do in να σου στείλω? Why not να στείλω σε εσένα?

Σου is the weak (clitic) indirect object pronoun for σε εσένα = to you (singular).

να σου στείλω = to send to you
να στείλω σε εσένα = to send to you (more emphatic)

In normal speech, Greeks strongly prefer the clitic pronoun:

Θα σου στείλω ένα email. = I will send you an email.
Μπορώ να σου στείλω μερικές ασκήσεις. = I can send you some exercises.

Σε εσένα is used for emphasis or contrast:

Όχι σε αυτόν, σε εσένα θέλω να στείλω τις ασκήσεις.
= Not to him, to you I want to send the exercises.

Why does σου come before στείλω and not after?

In Greek, weak object pronouns (like μου, σου, του, της, μας, σας, τους) normally go:

before a single finite verb in simple tenses:
- Σου γράφω. = I’m writing to you.
between the helping verb and να / other non‑finite verb constructions:
- μπορώ να σου στείλω
- θέλω να σου πω

So:

βεβαίως μπορώ να σου στείλω is normal
βεβαίως μπορώ να στείλω σου is wrong

What are μερικές ασκήσεις grammatically? Why is μερικές in that form?

Ασκήσεις is:

from η άσκηση = exercise
feminine, plural, accusative (direct object of να στείλω)

Μερικές is:

the feminine plural form of μερικός meaning several / some
it must agree with ασκήσεις in gender, number, and case:
μερικές ασκήσεις = some exercises
(fem. plural accusative + fem. plural accusative)

If the noun changed, μερικές would also change:

μερικά βιβλία (neuter plural) = some books
μερικοί φίλοι (masc. plural) = some friends

Is there any difference between μερικές ασκήσεις and κάποιες ασκήσεις?

Both mean some exercises, but with a small nuance:

μερικές ασκήσεις = some/several exercises (a few, not all, more neutral)
κάποιες ασκήσεις = some exercises (often with a slight feeling of unspecified / certain ones)

In your sentence, either could work; μερικές ασκήσεις is a very natural, neutral choice.

Why is it θέλεις and not θέλετε? How would I say this politely to someone I don’t know well?

Θέλεις = you want (2nd person singular, informal you)
Θέλετε = you want (2nd person plural, used for you plural or polite singular)

Your sentence is addressing one person informally (a friend, someone your age, etc.).

To be polite/formal to one person, you’d say:

Αν θέλετε βοήθεια με τα ελληνικά, βεβαίως μπορώ να σας στείλω μερικές ασκήσεις.

Changes:

θέλεις → θέλετε
σου → σας (to you, formal or plural)