нужно указать время каждого предложения и обозначить залог (active/passive) 1. I have attended lectures on history since May. 2. I attended lectures on history in May. 3. He has entered the Institute this year. 4. He entered the Institute last year. 5. Have you passed your examination? 6. Did you pass your examination on Friday well? 7. He has already returned to Moscow. 8. He returned to Moscow five days ago. 9. They haven't received any good results. 10. They didn't receive any good results when they worked with this type of equipment. 11. The temperature has been maintained at the point of 20 degrees since the beginning of the experiment. 12. During the experiment the temperature was maintained at the point of 20 degrees. 13. Has the new apparatus been already installed in the laboratory? 14. When was the new apparatus installed in the laboratory? 15. The new apparatus has already been installed.

Do you know where the Mississippi River is?
THE is the definite article.   when you have ONE of something that is definite, you use THE.  there is only one mississippi river, so you must use 'the'.

'an' is an indefinite article, not appropriate. if you have one of something thats not specific such as 'an apple'. 

He will be twenty in a month.
'in a month' says this is in the future, so you need a future tense verb
'am' goes with 'I' always  (I am ...)
'is' is present tense, but you could say 'he is going to be twenty in a month'

We might go to Peru next year.  We're not sure.
'not sure' means it may not happen. 'might' is also uncertain
so 'should' means we need to do something

that's the woman whose son is an actor.
i am not sure why, just that this one is correct

This afternoon, we are going sandboarding
a) and b) are the same answer
'this afternoon' means future tense
'going to' states a plan or intention, where 'will' is used in a different sense, as in a promise or request for help

i'm bored of camping trips.  let's go on a safari
'for' is definitely wrong
i have heard 'from' used, but i suspect it is not proper grammar

извините за все английский, мой руский не достаточно хорошо.

1. When I  was looking out of the window, I  saw John.

2.  Have you ever played the piano since you left school?

3. I  haven't seen him for two days.

4. When he  was trying to open the door, he dropped his key.

5. They have been living in this house since 1987.

6. My father  was washing his car while my mother and I  were preparing dinner.

7.  Did you  meet her yesterday?

8. Mary  has been in London for three days.

9. The headmaster  entered the classroom when they  were writing their exams.

10. He  bought a new car last week.

11. I think that they  will arrive tomorrow morning.

12. Last Wednesday they  played chess after they  had done their homework.