1) To answer the first question, the phrase "I have to study for the school" seems incomplete. However, based on the context, it appears that the missing word could be "exam" or "test." To confirm this, you can ask the person who wrote the text.
As for the rest of the sentence, it seems like a list of activities the person needs to do. There are various possibilities for how to complete it. Here is one possible completion:
"I can't come because I have to study for the school exam, study physics for tomorrow's test, look after my brother, clean my room, and go to the dentist's."
2) In the second question, the word "already" seems to be out of place. It would make more sense to place it before the verb "have." Here is a revised version of the sentence:
"I already have an appointment with Peter. Where shall I place already?"
3) The third question seems to be suggesting alternatives to a plan or activity. To complete the sentence, you can insert the suggested activities after each phrase. Here are a few possibilities:
"Why don't we go for a motorbike ride, a bike ride, or go sightseeing? Alternatively, we could go for a walk in the city centre."
4) In the fourth question, the use of the indefinite article "a" before "newspaper" and the omission of an article before "cigarettes" is correct. It is common to say "get a newspaper" or "get cigarettes" without using the definite article "the." This is because the speaker is referring to any newspaper or any cigarettes in general, not a specific one.