American or British slangs/idoms?

[Tortoise]

1. It is believed that the thief escaped in a stolen car. Which has the same meaning?
a) The thief is believed to escape in a stolen car.
b) The thief is believed to have escape in a stonlen car.

Another sentence:
It is believed that Einstein invented E = mc^2.

So the sentence which has same meaning is:
Einstein is believed to invent E = mc^2 ?

2. If you see John tomorrow, _____ you mind ______ him to get in touch with me?
a) will..... reminding
b) would..... reminding

3. Words as pull an all-nighter, cram, flunk, goof off, ace a test, hit the books, sluff class, be a whiz at, flying colors, hang in there are American or British slangs/idoms?

[Yankee]

Hi Tortoise

My comments are in blue in the quote:

[Tortoise]

Thank you for your help, Yankee. But I can not make out the tense of the sentence.

1. If "The thief is believed to escape in a stolen car".
= "The thief is believed to have escaped in a stolen car", does it refer The thief has escaped in a stolen car.
Also, if "Einstein is believed to invent E=mc^2" = "Einstein is believed to have invented E=mc^2", does it alsom refer that Einstein has invented E=mc^2?

2. I want to know that:
People say that John is a mad man
= It is said that John is a mad man
= John is said to be a mad man or John is said to have been a mad man?

Tortoise.

[Yankee]

Hi Tortoise

My comments are in blue inside the quote:

[Tortoise]

Thank you very much, Yankee. I realise that my grammar is not very good

Tortoise