Learn Hardcore Greek: Όταν είμαι άρρωστος, δεν έχω καθόλου όρεξη για φαγητό. - When I am sick, I don't feel like eating at all.

είμαι can only mean I am, so εγώ is not needed.
Όταν είμαι άρρωστος is the normal, natural way to say this.
You only add εγώ for emphasis, e.g. Όταν εγώ είμαι άρρωστος… (“When I am sick…” as opposed to someone else).

Why is είμαι (present) used after Όταν? Could it be another tense?

Όταν + present tense here expresses a general or habitual situation:

Όταν είμαι άρρωστος, δεν έχω…
= Whenever / When(ever) I’m sick, I don’t have… (a general rule about you)

If you were talking about a single, specific future time, you’d more likely use θα:

Όταν θα είμαι άρρωστος is rare and sounds awkward; more natural is
Όταν αρρωστήσω, δεν θα έχω όρεξη…
(When I get sick, I won’t have appetite…)

Why is άρρωστος masculine? How would it change if the speaker is a woman?

άρρωστος is an adjective and agrees with the gender and number of the subject:

Masculine singular: άρρωστος – Όταν είμαι άρρωστος… (a man speaking)
Feminine singular: άρρωστη – Όταν είμαι άρρωστη, δεν έχω καθόλου όρεξη… (a woman speaking)
Neuter singular: άρρωστο (for neuter nouns, e.g. το παιδί είναι άρρωστο)
Plural: άρρωστοι (masc.), άρρωστες (fem.), άρρωστα (neuter)

So you must adjust άρρωστος according to who is “sick.”

What exactly does όρεξη mean here? Is it just “appetite”?

In this sentence, όρεξη means appetite (for food).

Common meanings of όρεξη:

Appetite / desire for food
- Δεν έχω όρεξη για φαγητό. – I have no appetite for food.
Mood / desire to do something (not only eat)
- Δεν έχω όρεξη να διαβάσω. – I’m not in the mood to study.
- Έχω όρεξη για βόλτα. – I feel like going for a walk.

So όρεξη is broader than just physical hunger; it’s often “desire / mood” as well.

What does καθόλου add? Isn’t Δεν έχω όρεξη για φαγητό enough?

καθόλου adds emphasis: not at all / no … whatsoever.

Δεν έχω όρεξη για φαγητό. – I don’t have appetite for food.
Δεν έχω καθόλου όρεξη για φαγητό. – I have absolutely no appetite for food.

So καθόλου intensifies the negation, like “at all” or “zero.”

Can καθόλου also be used in positive sentences?

In modern everyday Greek:

With negatives, καθόλου = at all
- Δεν πεινάω καθόλου. – I’m not hungry at all.
In questions, it can mean at all / any (often implying “even a little”):
- Έχεις καθόλου χρόνο; – Do you have any time (at all)?

Using καθόλου in clearly positive statements like Έχω καθόλου χρόνο is unusual today; it sounds old‑fashioned or literary. Usually καθόλου appears with negation or in questions.

Could καθόλου go in a different position, like Δεν έχω όρεξη καθόλου για φαγητό?

Yes, καθόλου is fairly flexible in placement. All of these are possible:

Δεν έχω καθόλου όρεξη για φαγητό. (most common)
Δεν έχω όρεξη καθόλου για φαγητό.
Δεν έχω όρεξη για φαγητό καθόλου.

Moving it later in the sentence can sound slightly more emphatic, but all are correct and natural.

Why is it για φαγητό and not για το φαγητό?

Here για φαγητό means for food / to eat (in general), not a specific dish.

για φαγητό = for food / for eating (general concept)
- Όρεξη για φαγητό – appetite for food.
για το φαγητό would usually mean about the (specific) food or for the (particular) meal
- Μιλήσαμε για το φαγητό. – We talked about the food.
- Τα φάρμακα είναι για το φαγητό. – The medicines are for the meal (to take with food).

So no article is used when you mean food in a general, abstract way.

How is δεν used here, and what’s the difference between δεν and μη(ν)?

In δεν έχω καθόλου όρεξη, δεν is the normal negation for indicative verbs:

δεν
- verb in the indicative: δεν έχω, δεν είμαι, δεν θέλω.

μη(ν) is used mainly:

Before subjunctive (with να, ας, etc.):
- να μην φάω, ας μην πάμε
In some fixed expressions and imperatives:
- Μην ανησυχείς. – Don’t worry.

So here, because έχω is just a simple present indicative, the correct negation is δεν.

Could I say αν είμαι άρρωστος instead of όταν είμαι άρρωστος? What’s the difference?

You can say αν είμαι άρρωστος, but the meaning shifts:

Όταν είμαι άρρωστος, δεν έχω…
= When(ever) I’m sick, I don’t have…
(temporal – a general rule about what happens when you are sick)
Αν είμαι άρρωστος, δεν θα έρθω.
= If I’m sick, I won’t come.
(conditional – maybe I’ll be sick, maybe not)

In your sentence, we’re talking about what always happens when you’re sick, so όταν is more natural than αν.

Could I say Δεν έχω όρεξη να φάω instead of όρεξη για φαγητό?

Yes, that’s a very natural alternative, and the meaning is almost the same.

Δεν έχω καθόλου όρεξη για φαγητό.
– I have no appetite for food.
Δεν έχω καθόλου όρεξη να φάω.
– I don’t feel like eating at all.

Patterns:

έχω όρεξη για + noun (φαγητό, καφέ, βόλτα…)
έχω όρεξη να + verb (φάω, βγω, διαβάσω…)

Both are very common.

How do you pronounce the sentence, especially άρρωστος and όρεξη?

Approximate phonetic transcription:

Όταν είμαι άρρωστος, δεν έχω καθόλου όρεξη για φαγητό.
[Ótan íme Árrostos, then Écho kathÓlou Óreksi ya fayiTÓ]

Key points:

άρρωστος: Á-rr-o-stos – double ρ (rr) is slightly rolled.
όρεξη: Ó-re-xi (the ξ is like “ks”).
φαγητό: fa-yi-TÓ – the γη is like “yi”.

Stress falls where the written accent is: Όταν, είμαι, άρρωστος, δεν, έχω, καθόλου, όρεξη, φαγητό (each has exactly one stressed syllable).