Correct my sentences. Word-translate-example

Remain - оставаться - I resolved to remain at home. 
Receive - получать, принимать - She received a ticket to the theatre (на ангийском обычно уточняют, а не просто говорят "в театр", как что тут я бы сказала "She received a ticket to the play tonight).
Request - запрашивать, просить - They requested a blanket for their room.
Suffice - хватать, быть достаточным - Food stock will suffice for 2 days.
Assemble - собирать, собираться - My daughter assemble to jump from the bridge. Assemble используется не в смысле "собираться с силами", а в смысле "собирать все нужное", поэтму Я бы предложила фразу "Му daughter assempled her backpack to head for school" 
Resolve - разрешать, решать - Mary resolve me play with her dogs. Resolve означает решать в смысле "он решил найти работу" или "он решил свои проблемы", так что я бы предложила фразу "He resolved most of his problems this year"
Prevent - предотвращать - The doctor prevents the disease. Prevent - это предотвращать  в смысле предтвращать до того, как что-то наступило, так что Я бы предложила "The vaccine prevents the dшsease".
Operate - действовать - They operate so fast. Все верно!
Perish - погибать - The soldier perished in the war.
Vanish - исчезать - The spot vanished after washing. Все верно!

Надеюсь. это помогло!

A funny thing I used to believe

When I was a child, I used to believe a funny thing. When I had a ride in my father's car which my father drove, I noticed that however much we moved, I could see the moon. I asked my father why the moon could be seen. My father answered that it's because the moon was following us. I believed that the moon was following us at that time. Do you have funny things you used to believe?

Explanation: "could see the moon" and "the moon couldn't be seen" mean opposite things. If you mean that the moon was visible both times, then you shouldn't put "could" in a negative form

Plus, the phrase "My father answered that because the moon was following us" sounds strange and means a different thing without "it's" or "that's" between "that" and "because". Without "it's" or "that's" the phrase means "My father answered that as a consequence of the moon was following us" which sounds as a strange unfinished phrase

You may be sure means "you may be certain". I can explain it word by word: "You may be", as a form that allows you to do something or ensures you in doing it. "You may be sure" means that you are allowed to be sure, that there's no mistake in being sure. So, in the phrase "and she wasn't best pleased, you may be sure, when the prince told her that he was going to marry her stepdaughter..." it means "you can be certain that she wasn't best pleased when the prince told her that he was going to marry her stepdaughter ". Hoping to be clear, Helen