Could you please check these sentences?

Thank you.

1) Make yourself at home and help yourself to a cup of tea.
After waking up it takes me a while to get up.
2) Have you woken the child up?
She apologized to me for arriving late/for not doing her homework/for leaving her book at home.
3) She complained to the headmaster about being reprimanded in the class register.
4) She sat down (on the chair) and took (picked is a mistake?) her English book out of the rucksack.
5) I wonder if I will be able to pass my driving test.
She congratulated with me on passing her driving test.

1) Make yourself at home and help yourself to a cup of tea. <~~OK

After waking up, it takes me a while to get up.

2) Have you woken the child up?
(I'd say, "Have you awakened the child?" or "Did you wake the child up?")

She apologized to me for arriving late/for not doing her homework/for leaving her book at home. <~~OK

3) She complained to the headmaster about being reprimanded in the class register. <~~OK

4) She sat down and took her English book out of the rucksack.
(You could use "picked" if you mean she picked it up off the table or desk or floor or ... )

5) I wonder if I will be able to pass my driving test. <~~OK

She celebrated for passing her driving test.

After waking up, it takes me a while to get up.

(The repetition of "up" in this sentence sounds awkward. How about this: "After awakening, it takes me a while to get up" or "After waking up, it takes me a while to get out of bed.")

Sure, let's check these sentences and make any necessary corrections.

1) Make yourself at home and help yourself to a cup of tea.
After waking up it takes me a while to get up.

These sentences are correct as they are.

2) Have you woken the child up?

This sentence is correct as it is.

She apologized to me for arriving late/for not doing her homework/for leaving her book at home.

These sentences are correct and convey different situations where the person is apologizing for various reasons.

3) She complained to the headmaster about being reprimanded in the class register.

This sentence is correct as it is.

4) She sat down (on the chair) and took (picked is a mistake?) her English book out of the rucksack.

In this sentence, if you want to use the word "picked," it would be more appropriate to say "She picked up her English book from the rucksack." However, the sentence is already correct using the phrase "took her English book out of the rucksack."

5) I wonder if I will be able to pass my driving test.

This sentence is correct as it is.

She congratulated with me on passing her driving test.

In this sentence, there are a couple of errors. It should be "She congratulated me on passing her driving test." Also, based on the context, it's likely that the person who passed the driving test is the one being congratulated, so it should be "on passing my driving test" instead of "her driving test."

Corrected sentence: She congratulated me on passing my driving test.

Overall, the sentences look good with some minor corrections. Well done!