1) I...already...doing housework. (finish).

2) By the time she got home her children...already...their homework. (do).

3) We...working yet. (start)

4) ...you...this film.(see)

5) Next year I...here for 20 years.(work)

6) When I saw her last time she...already...her hairstyle.(change)

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.I have finished my homework. Can I go out now.
2. I was ill three month ago.
3.My hobby is fishing. I have caught a lot of fish.
4. I played basketball when I was younger, but I don't play now.
5. I have already seen "Shrek"
6. Julie has been ill since Tuesday.
7.I haven't seen Josh since 1998.
8. We stayed at our grandparents for three days. We arrived home yesterday.
9. The dog went to sleep an hour ago.
10.I have had a cat for two years. Its (не it is) name is Willis.
11.I waited for a bus for twenty minutes. Then I decided to walk.