Προτιμώ να βάζω αντηλιακό κάθε δύο ώρες παρά να καίγομαι στον ήλιο.

Because Greek usually does not use an infinitive the way English does.
So where English says I prefer to apply... rather than get burned..., Greek uses να + verb for both actions:

• να βάζω
• να καίγομαι

After προτιμώ, this is very normal:
Προτιμώ να... παρά να... = I prefer to... rather than to...

After να, Greek verbs often appear in forms that look like the present tense, but what really matters here is aspect, not just time.

In this sentence:

• να βάζω = ongoing/repeated action, so to be applying / to apply regularly
• να καίγομαι = ongoing/repeated situation, so to be getting burned

This fits the meaning well because the sentence talks about a habit or repeated preference, not a one-time action.

Yes, but it changes the nuance.

• να βάζω = imperfective aspect, focusing on a repeated or ongoing action
  → to keep applying / to apply regularly
• να βάλω = perfective aspect, focusing on a single complete action
  → to put on once

Since the sentence includes κάθε δύο ώρες (every two hours), να βάζω is the more natural choice, because it describes a repeated habit.

Προτιμώ means I prefer.

A very common pattern is:

• Προτιμώ να... = I prefer to...
• Προτιμώ Χ παρά Υ = I prefer X rather than Y
• Προτιμώ να... παρά να... = I prefer to... rather than to...

So this sentence follows a very standard structure.

Yes. In this kind of sentence, παρά means rather than or than after a comparison of preference.

So:

• Προτιμώ να βάζω αντηλιακό παρά να καίγομαι στον ήλιο. = I prefer to put on sunscreen rather than get burned in the sun.

This is a common use of παρά after προτιμώ.

Αντηλιακό means sunscreen / sunblock.

It is originally an adjective meaning something like sun-protective, but very often it is used on its own as a noun:

• το αντηλιακό = the sunscreen

You may also hear:

• αντηλιακή κρέμα = sunscreen cream

But in everyday speech, just αντηλιακό is extremely common.

Yes, βάζω basically means put, but Greek uses it very naturally for things you put on your body, including:

• βάζω αντηλιακό = put on/apply sunscreen
• βάζω κρέμα = put on/apply cream
• βάζω άρωμα = put on perfume

So this is a normal and idiomatic choice.

It means every two hours.

Breakdown:

• κάθε = every
• δύο ώρες = two hours

So literally: every two hours.

Greek often uses κάθε + time expression this way:

• κάθε μέρα = every day
• κάθε εβδομάδα = every week
• κάθε δύο ώρες = every two hours

Because δύο means two, so the noun must be plural:

• μία ώρα = one hour
• δύο ώρες = two hours

Since the phrase is κάθε δύο ώρες, the plural is required.

Καίγομαι literally means I burn / I am getting burned / I get burned, and yes, it is a middle-passive form.

In this sentence it means something like:

• to get sunburned
• to be burned

So:

• να καίγομαι στον ήλιο = to get burned in the sun

Greek often uses this middle-passive form where English uses an active-looking phrase like get burned.

Because στον is the contracted form of:

• σε + τον = στον

So:

• στον ήλιο = in the sun

This kind of contraction is standard in modern Greek:

• στο = σε + το
• στη / στην = σε + τη(ν)
• στον = σε + τον

Here it means in the sun.

Greek commonly uses στον ήλιο to express being exposed to sunlight. It is the normal idiomatic choice in this context.

Because Greek usually does not need an explicit subject pronoun when the verb ending already shows the subject.

• Προτιμώ already means I prefer

So Greek can leave out εγώ (I) unless it is needed for emphasis or contrast.

The structure is:

• Προτιμώ = I prefer
• να βάζω αντηλιακό κάθε δύο ώρες = to apply sunscreen every two hours
• παρά να καίγομαι στον ήλιο = rather than get burned in the sun

So the pattern is:

Προτιμώ + να-clause + παρά + να-clause

This is a very common and natural Greek structure.

You could add εγώ for emphasis:

• Εγώ προτιμώ να βάζω αντηλιακό κάθε δύο ώρες παρά να καίγομαι στον ήλιο.

That would sound like:

• I prefer to apply sunscreen every two hours rather than get burned in the sun.

But without εγώ, the original sentence is already perfectly natural.

A rough pronunciation guide is:

Pro-ti-MO na VA-zo anti-ya-LI-ko KA-the THI-o O-res pa-RA na KE-yo-me ston I-lio

A few helpful notes:

• ώ in προτιμώ is stressed: pro-ti-MO
• βάζω is stressed on the first syllable: VA-zo
• αντηλιακό is stressed on the last syllable: anti-ya-li-KO
• καίγομαι is stressed on KAI: KE-yo-me / KAI-yo-me depending on how narrowly you represent it
• ήλιο is stressed on I: I-lio

Yes, it is natural.

A native speaker might also say similar versions such as:

• Προτιμώ να βάζω αντηλιακό κάθε δύο ώρες, παρά να καώ στον ήλιο.
• Προτιμώ να βάζω αντηλιακό παρά να καίγομαι στον ήλιο.

But your sentence is perfectly good Greek, especially because κάθε δύο ώρες matches the repeated-action idea of να βάζω very well.