wǒ tài lèi le, kuài shuìzháo le.

太 + adjective + 了 is a very common pattern meaning so / really / too ... with strong emotion.

So 太累了 means so tired.

太 is not always negative. It just shows a high degree:

• 太好了！ = So great!
• 太贵了！ = Too expensive / so expensive!

In this sentence, it sounds negative because 累 itself is negative.

In 太 + adjective + 了, the 了 is part of a very common set pattern.

So 太累了 is much more natural than just 太累.

This 了 often adds a sense of:

• the speaker’s strong feeling
• a current situation
• sometimes a changed state

So 我太累了 feels like I’m so tired! rather than a flat dictionary-style statement.

In 睡着了, the 了 shows a change into a new state: going from not asleep to asleep.

So:

• 睡着 = to fall asleep / be asleep as a result
• 睡着了 = fell asleep / has fallen asleep

In this sentence, because of 快, 快睡着了 means almost about to fall asleep or on the verge of falling asleep.

A useful learner shortcut is to treat 睡着了 as one chunk.

Here, 快 does not mean fast.

Before a verb or verb phrase, 快 often means:

• soon
• almost
• about to

So 快睡着了 means almost falling asleep or about to fall asleep.

If you wanted to say fell asleep quickly, that is a different idea:

• 很快就睡着了 = fell asleep quickly

睡着 means to fall asleep or to end up asleep.

It is different from:

• 睡觉 = to sleep / go to bed
• 睡 = to sleep
• 睡着 = to actually drift off and reach the asleep state

So:

• 我要睡觉了 = I’m going to sleep / go to bed.
• 我睡着了 = I fell asleep.

Because 着 has multiple pronunciations in Chinese.

Common ones include:

• zhe: aspect marker, as in 看着
• zháo: result complement, often meaning manage to reach / come into a state
• zhuó and zhāo in other words and set uses

In 睡着, it is zháo because it shows a result: the person reaches the state of being asleep.

So:

• 睡着 shuìzháo = fall asleep

No. It means the speaker is very close to being asleep.

So 快睡着了 is more like:

• I’m about to fall asleep
• I’m almost asleep

If the speaker is already asleep, you would not normally say this about yourself in the moment, because an asleep person is not talking. But about someone else, you could say:

• 他睡着了。 = He fell asleep / He is asleep now.

Because in Chinese, adjectives can often act as the predicate by themselves.

So Chinese says:

• 我累。 not
• 我是累。

Also, Chinese usually likes some kind of degree word with adjectives in simple statements, such as:

• 很
• 太
• 真

That is why 我太累了 sounds very natural.

Yes. Both are natural.

• 快睡着了 = almost asleep / about to fall asleep
• 快要睡着了 = about to fall asleep
• 要睡着了 = about to fall asleep

The differences are small. 快要 is a little more explicit about about to.
In everyday speech, all of these can work.

Yes, but the feeling changes.

• 我很累，快睡着了 = I’m very tired and almost falling asleep.
• 我太累了，快睡着了 = I’m so tired, I’m about to fall asleep.

很累 is more neutral.
太累了 sounds stronger and more emotional.

So the original sentence feels more vivid and dramatic.

The sentence has two closely connected clauses:

• 我太累了
• 快睡着了

The comma links them naturally, like:

• I’m so tired, I’m about to fall asleep.

Chinese often uses commas to connect related clauses where English might also use a comma or split into two sentences.

Yes, if the subject is already clear from context.

For example, in conversation, someone might simply say:

• 太累了，快睡着了。

That sounds very natural.

Chinese often drops subjects when they are obvious.