I have a few more doubts on these sentences. Thank you for your help.

1)The bus, by which I usually come to school, was late this morning.
2)The briefcase, which you put on the book-shelf, is Peter's.
3)You'd better/should (put)/If I were you (in your place), I'd put a bandage on your bruise/on it/ on (Are the three alternatives correct?)
I had a headache/stomachacte/toothache/backache (Do you know others?)
4) My stomach hurts/aches, I have a pain in my stomach (belly?). My stomache is sore (???)
5)I had a rash (on my skin). The doctor prescribed antihistamine to me. (but: I was prescribed antihistamine).
5) I'm allergic to cat's hair (??). I sneeze whenever a cat come near me.
6) We stopped at a motorway restaurant for lunch (late in the evening/early in the morning).

1 - OK

2 - If there is only one briefcase and you put it on the bookshelf, then this sentence is fine. If there are several briefcases and the only one put on the bookshelf is Peter's, then remove the commas.

3 - yes, all are correct

4 - period after "aches" -- all else is fine

5 - no need for "to me" ("I was prescribed" is incorrect.)

should be "cat's fur" -- also "comes" not "come"

6 - OK

1 is kind of awkward. I would change come to take.

If you change "come" to "take" in #1, be sure to also delete "by."

1) The bus, by which I usually come to school, was late this morning.

To find the correct answer, we need to identify the function of the phrase "by which I usually come to school." This phrase is a relative clause that provides additional information about the noun "bus." The relative pronoun "which" is used to connect the relative clause to the noun. In this case, "by which" indicates the method or means by which the speaker usually comes to school.
Therefore, the correct answer is that the bus, which is usually the method of transportation the speaker uses to come to school, was late this morning.

2) The briefcase, which you put on the book-shelf, is Peter's.
Similar to the previous sentence, we have a relative clause that provides additional information about the noun "briefcase." In this case, the relative clause "which you put on the book-shelf" tells us where the briefcase was placed. The relative pronoun "which" is used to connect the relative clause to the noun.
Hence, the correct interpretation is that the briefcase, which was placed on the book-shelf by you, belongs to Peter.

3) You'd better/should (put)/If I were you (in your place), I'd put a bandage on your bruise/on it/ on.
All three alternatives are correct, but they slightly differ in emphasis or style.
"You'd better put a bandage on your bruise" is a more direct and authoritative statement, suggesting that it is the most advisable course of action.
"You should put a bandage on your bruise" is a softer recommendation, implying that it is a good idea to do so.
"If I were you, I'd put a bandage on your bruise" is a hypothetical statement, where the speaker is imagining themselves in your place and saying they would take this action.

4) I had a headache/stomachache/toothache/backache.
These are all common examples of bodily pains or discomforts. Other examples might include earache, joint pain, muscle ache, or menstrual cramps, among others.

5) My stomach hurts/aches, I have a pain in my stomach (belly?). My stomach is sore.
All three alternatives are correct and describe discomfort or pain in the abdominal area. "Stomach hurts" and "stomach aches" are interchangeable and commonly used phrases. "I have a pain in my stomach (belly)" describes the presence of pain specifically in the stomach region. "My stomach is sore" implies a general feeling of tenderness or sensitivity in the stomach area.

6) I had a rash (on my skin). The doctor prescribed antihistamine to me. (but: I was prescribed antihistamine).
Both sentences are correct, but they have slightly different structures. "The doctor prescribed antihistamine to me" is a more common way to express that the doctor gave you a prescription for antihistamine medication. "I was prescribed antihistamine" is passive voice, where the subject (I) receives the action of the verb (prescribed).

7) I'm allergic to cat's hair (??). I sneeze whenever a cat comes near me.
The correct sentence should be "I'm allergic to cat hair" without the apostrophe. This means that you have an allergic reaction when exposed to cat hair. Additionally, "whenever a cat comes near me" implies that your sneezing occurs every time a cat approaches you.

8) We stopped at a motorway restaurant for lunch (late in the evening/early in the morning).
The sentence itself doesn't explicitly state when the stop occurred, but the phrase "late in the evening/early in the morning" provides two possible time options. It suggests that the stop at the motorway restaurant for lunch could have taken place either late in the evening or early in the morning.