1. He admitted driving carelessly.

2. He admitted having driven caressly.
(Are both grammatical? What's the difference?)

3. He admitted having me the girl.
4. He admits having eaten the bread.

5. He admitted breaking the window.
6. He admitted having broken the window.
(What about these ones? What's the difference in meaning?)

1 and 2 mean the same thing. The only difference is in the tense of the participle, but the meaning is the same.

3 makes no sense.

4 is fine.

5 and 6 are like 1 and 2 -- they're fine.

The only differences I can see in meaning for 1&2 and 5&6 could be that 1 and 5 were spoken right after the incident, while 2 and 6 were spoken after a period of time had passed since the incident (driving or breaking).

1. He admitted driving carelessly.

2. He admitted having driven caressly.

3. He admitted having met the girl.
4. He admits having eaten the bread.

5. He admitted breaking the window.
6. He admitted having broken the window.

* Thank you for your help. I corrected an error.

1. Yes, the sentence "He admitted driving carelessly." is grammatical.

2. However, the sentence "He admitted having driven carelessly." is not grammatically correct. The correct version would be: "He admitted to having driven carelessly."

3. The sentence "He admitted having me the girl." is not grammatically correct. It seems like there may be a mistake in the structure of the sentence. A corrected version could be: "He admitted introducing me to the girl."

4. The sentence "He admits having eaten the bread." is grammatically correct.

5. The sentence "He admitted breaking the window." is grammatically correct. It implies that the person admitted to the action of breaking the window.

6. Similarly, the sentence "He admitted having broken the window." is also grammatically correct. It also implies that the person admitted to the action of having broken the window, specifically suggesting that the breaking of the window occurred before the admission was made.