Could you check these very few sentences. I also wanted to know why the sentence "He is said to send her messages" is wrong. Isn't it equivalent to "they say he always sends her messages"? Thank you for helping me.

1) A make-up artist is someone who puts make-up on actors' and actresses' faces.
Can you say:
2) A group of teenagers like wearing baggy jeans.
Another group liks wearing baseball caps.
3) The rest of teenagers likes wearing washed-out jeans.

1. OK

2. Since "group" is singular, you must make the verb singular, too: "likes".
In the second sentence, check the spelling of "likes".

3. Since "rest" in this case is a plural, how will you fix the verb?

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The "he is said" sentences are awkward. Try this phrasing:

It is said that he sends her messages each day.

It is said that he will send her messages every day.

It is said that he sent her messages every day of her life.

(Or is there another idea you want to convey?)