Thank you very much for suggesting me such useful sites! I still have a few more sentences to prepare for tomorrow. I really hope you can have a look at them, too. (just say "yes" if it is possible)

1 ) Another feature of the epic poem is that it contains formulas (can you say “is the use of formulas”?)
2)At that time people followed Ptolemy’s theories, according to which the planetary system was Earth-centred. Can you also say: The planetary system was believed to be earth-centred in accordance with the theory of Ptolemy.?
3 ) He eventually succeeds (can you start with eventually, he succeeds) in killing a monster.
4) The expression “lord of friends” is used to rename/describe/refer to (are they all possible?) Beowulf.
5 ) Kennings are metaphorical expressions in which a word is substituted for by a compound word, e.g. “scholar’s home” for “school” . (is it all right to use e.g. or “as for example” in this case?)
6) A sentence is incomplete and another does not make sense at all since you chose a wrong conjunction.
7) Middle Age society (correct: medieval society) believed in Ptolemy’s theory (or followed Ptolemy’s theory)
8) According to the Constitution of Clarendon, the king was the only one who could invest the bishops.
9) We went on holiday to have a rest/in order to/so as to have a rest/ so that we could have a rest/for a rest.
10) She was ill, yet/still she went to school. She was ill; she still went to school (is it possible?) .She was ill. However/Nevertheless/Nonetheless/even so/ In spite of that/Despite of that she went to school. She went to school. She was ill, though.
11) In spite of/despite her illness/being ill, she went to school. Although/even though/ in spite of the fact that she was ill, she went to school
12) Can you also say: She was ill, but she went to school all the same?

1. yes = formula (plural formulae in scientific use, formulas in informal use)

2. yes, especially the 2nd
3. yes, and even at the end
4. yes
5. yes, but you don't need "for" = substituted by...
6. One sentence is better than "A"
7. in parentheses better
8. yes
9. ye
10. yes
11. yes
12. yes

Sra (aka Mme)

Yes, it is possible for me to have a look at the sentences you have prepared for tomorrow. Please provide the sentences one by one, and I will help you with any necessary edits or suggestions.

1) Another feature of the epic poem is that it contains formulas.
- Yes, "is the use of formulas" can also be used in this sentence. Either way, both phrases are correct.

2) At that time people followed Ptolemy’s theories, according to which the planetary system was Earth-centered.
- Yes, you can also say, "The planetary system was believed to be earth-centered in accordance with the theory of Ptolemy." Both variations are correct.

3) Eventually, he succeeds in killing a monster.
- This sentence is already well-written, starting with "Eventually, he succeeds."

4) The expression "lord of friends" is used to rename/describe/refer to Beowulf.
- Yes, all three options are possible. You can say, "The expression 'lord of friends' is used to rename/describe/refer to Beowulf."

5) Kennings are metaphorical expressions in which a word is substituted for by a compound word, e.g., "scholar's home" for "school."
- Yes, it is perfectly fine to use "e.g." in this case. "E.g." stands for "exempli gratia," which means "for example."

6) A sentence is incomplete, and another does not make sense at all, as you chose a wrong conjunction.
- This sentence is already well-written, noting the incorrect use of the conjunction.

7) Medieval society believed in Ptolemy’s theory (or followed Ptolemy's theory).
- Yes, you can say either "believed in Ptolemy's theory" or "followed Ptolemy's theory." Both options are correct.

8) According to the Constitution of Clarendon, the king was the only one who could invest the bishops.
- This sentence is already accurate and does not require any changes.

9) We went on holiday to have a rest/in order to/so as to have a rest/so that we could have a rest/for a rest.
- Yes, all variations are possible and correct. You can say, "We went on holiday to have a rest," "We went on holiday in order to have a rest," "We went on holiday so as to have a rest," "We went on holiday so that we could have a rest," or "We went on holiday for a rest."

10) She was ill; she still went to school. She was ill. However/Nevertheless/Nonetheless/Even so/In spite of that/Despite that, she went to school.
- Yes, it is possible to use any of the provided conjunctions. All variations are correct, such as "She was ill. However, she went to school," "She was ill. Nevertheless, she went to school," "She was ill. Nonetheless, she went to school," "She was ill. Even so, she went to school," "She was ill. In spite of that, she went to school," or "She was ill. Despite that, she went to school."

11) In spite of/Despite her illness/being ill, she went to school. Although/even though/In spite of the fact that she was ill, she went to school.
- Yes, all variations are possible and correct. You can say, "In spite of her illness, she went to school" or "Despite being ill, she went to school," "Although she was ill, she went to school" or "Even though she was ill, she went to school," or "In spite of the fact that she was ill, she went to school."

12) She was ill, but she went to school all the same.
- Yes, this sentence is correct.