Спасибо, я уже сыт.

In Russian, the verb to be is normally omitted in the present tense.

So:

• я сыт = I am full
• literally, Russian just says something like I full

This is completely normal. You do use forms of быть in other tenses:

• я был сыт = I was full
• я буду сыт = I will be full

But in the present tense, есть is not used here in standard modern Russian.

Сыт is the short form of the adjective, and that is the normal form used here.

Russian often uses:

• the full form of an adjective when it describes a noun: сытый человек = a full/satisfied person
• the short form when it states someone’s current condition: я сыт = I’m full

So in this sentence, сыт is the natural choice because it describes a current state.

Yes. It agrees with gender and number.

Forms:

• masculine: сыт
• feminine: сыта
• neuter: сыто
• plural: сыты

So:

• a man says Спасибо, я уже сыт.
• a woman says Спасибо, я уже сыта.
• a group could say Спасибо, мы уже сыты.

Уже means already.

In this sentence, it adds the idea of:

• I’m already full
• I’ve had enough already
• no more food is needed

Without уже:

• Спасибо, я сыт. = Thanks, I’m full.

With уже:

• Спасибо, я уже сыт. = Thanks, I’m already full.

It makes the refusal sound a little more natural in a food situation, because it suggests you have already eaten enough.

That is the most neutral and natural position here.

• я уже сыт = standard, neutral word order

Russian word order is flexible, but changing it can shift emphasis. For example:

• я уже сыт = neutral
• я сыт уже = possible, but sounds more marked or emphatic

For learners, я уже сыт is the best pattern to use.

Because Спасибо is functioning as a separate politeness formula, followed by a full clause:

• Спасибо, я уже сыт.

This is similar to English punctuation in:

• Thanks, I’m already full.

In standard writing, the comma is the normal choice.

Yes, it is natural, correct, and polite.

It works well when someone offers you more food and you want to decline politely.

If you want to sound a little warmer, you can expand it:

• Спасибо, я уже сыт. Очень вкусно.
• Большое спасибо, я уже сыт.

If the speaker is female:

• Спасибо, я уже сыта.

Sometimes, yes.

Russian often drops subject pronouns when the meaning is obvious from context. So in conversation you may hear:

• Спасибо, уже сыт.

That sounds casual and conversational. But for learners, keeping я is safer and clearer:

• Спасибо, я уже сыт.

Both are possible; the version with я is just more explicit.

Сыт is pronounced as one syllable: syt.

The tricky part is the vowel ы, which has no exact English equivalent. It is not the same as ee in see and not the same as i in sit.

A rough guide:

• keep your tongue farther back than for English ee
• pronounce a short, central/back vowel

Stress is easy here because the word has only one syllable:

• сыт

The whole sentence is stressed like this:

• спаси́бо, я уже́ сыт

Yes. That is also very natural.

The difference is:

• я сыт = focuses on your current state: I’m full
• я наелся = focuses more on the result of eating: I’ve eaten enough / I’ve had my fill

Both can be used at the table. Very roughly:

• я уже сыт = I’m already full
• я уже наелся = I’ve already eaten enough

If the speaker is female, it becomes:

• я уже наелась

By itself in a sentence like this, it is usually understood literally: you have eaten enough.

But forms of this word can also appear in figurative expressions, such as:

• сыт по горло = fed up, literally full up to the throat

Still, in Спасибо, я уже сыт, the normal interpretation is simply that the speaker does not want more food.