Learn Hardcore Ukrainian: Звичайно, вона прийде вчасно на зустріч. - Of course, she will arrive on time for the meeting.

Because Звичайно here is a parenthetical sentence adverb meaning of course. Such introductory words are set off by a comma in Ukrainian: Звичайно,, На жаль,, Можливо, etc. If звичайно were used differently (not as an aside), punctuation could vary, but sentence-initial as in this example it takes a comma.

Does звичайно ever mean usually? I’ve seen both meanings in dictionaries.

In modern Ukrainian, to say usually you should use зазвичай. Звичайно in this sentence means of course, certainly. While older or dialectal usage may blur them, keeping the distinction звичайно = of course vs зазвичай = usually is the safest choice for learners.

Could I replace звичайно with something else like звісно or авжеж?

Yes, common synonyms for of course include:

звісно (very common, neutral)
авжеж (colloquial, emphatic)
безперечно, певна річ (more formal/literary) All would fit here, with slight differences in tone: авжеж sounds a bit punchier; безперечно more formal.

What exactly is the tense/aspect of прийде?

Прийде is the simple future of the perfective verb прийти (to come). Perfective future = a single, completed event in the future. So it implies she will arrive (and the arrival will be accomplished). The imperfective partner is приходити (habitual/ongoing).

Could I say вона приходить or вона буде приходити instead?

Вона приходить = she comes/arrives (habitually, generally, or right now in a narrative), not a one-off future arrival.
Вона буде приходити = she will be coming (repeatedly/regularly in the future). To express a single future arrival, вона прийде is the natural choice.

How do you conjugate прийти in the future?

Perfective future (simple):

я прийду́
ти прийде́ш
він/вона/воно прийде́
ми прийде́мо
ви прийде́те
вони прийду́ть

Is прийти only for coming on foot? What about приїхати or прибути?

прийти originally implies coming (often on foot), but in everyday speech it’s used broadly for arrive/come, regardless of transport, unless you want to emphasize the mode.
приїхати explicitly means to arrive by vehicle.
прибути is more formal/official (to arrive), often used for trains, flights, schedules.

What does вчасно add exactly? Are there alternatives?

Вчасно means on time, punctually. Near-synonyms:

своєчасно (timely; a bit more formal)
пунктуально (loanword, formal/learned) Adjective: вчасний (timely). Don’t try to say часно—that’s not a word in this sense.

Is на зустріч the right preposition? Why not до зустрічі?

For motion toward an event, Ukrainian uses на + Accusative: прийти на зустріч, піти на лекцію, записатися на курс.
До зустрічі is a different construction with до + Genitive, meaning to/till a meeting, and it’s also the fixed farewell formula meaning See you!.

What’s the difference between на зустріч and назустріч?

на зустріч (two words) = to a meeting (the noun зустріч = a meeting). It takes Accusative: на зустріч.
назустріч (one word) = towards, to meet (someone/something). It usually takes Dative: назустріч мені = towards me.
They are not interchangeable.

Why is it на зустріч (Accusative) here and not на зустрічі (Locative)?

With на, Accusative indicates direction (to), while Locative indicates location (at):

Direction: прийти на зустріч (to a meeting) — Accusative.
Location: бути на зустрічі (at a meeting) — Locative.

Can I move words around? For example, вона прийде на зустріч вчасно or Вона, звичайно, прийде…

Yes. Ukrainian allows flexible word order for emphasis and rhythm:

Вона прийде вчасно на зустріч. (neutral)
Вона прийде на зустріч вчасно. (slight emphasis on being on time relative to the meeting)
Вона, звичайно, прийде вчасно на зустріч. (parenthetical in the middle)
Звичайно, вона прийде… (baseline from your sentence) All are grammatical; choose based on what you want to highlight.

Is the pronoun вона required, or can I omit it?

You can omit subject pronouns if context makes the subject clear: Прийде вчасно на зустріч. However, including вона is normal and avoids ambiguity, especially in short standalone sentences.

How do I pronounce the sentence? Where is the stress?

Stresses: Звича́йно, вона́ прийде́ вча́сно на зу́стріч.
Approximate pronunciation: [zvu-CHAi-no, vo-NA pryj-DE v-CHAS-no na ZU-strich].
Notes: Ukrainian в can sound like [ʋ]/[v]/[w] depending on position; й is a short y-glide; ч is [ch].

Could звичайно sound sarcastic?

Yes, intonation can make звичайно sound sincere or sarcastic, just like English of course. In writing, context or punctuation (like Звичайно…) may hint at irony.