Grammar

1) When we arrived, the guests had (already) finished dancing.

I guess you mean the guests were not dancing because the dancing was done earlier.

2) What's the matter? Why is the child crying?

Without the, I hear someone's name.  Why is Anna crying? Why is your friend crying? Why is the child crying?

3) -What are you looking for?

- I am looking for the comb. I left it on the table yesterday, but it isn't there now.

Correct, but the comb suggests it's a comb that everyone knows about. My comb might be better for telling us which comb.

4) I sat with Mr.Lane on the bus yesterday. We talked about work, and about our future plans. Mr. Lane thinks he will spend his summer in the mountains.

If you use tell/told, you need two objects: who was listening, and what was said.  We told each other about our work...

5) Henry seldom writes letter to his parents, but he rings them often. 

6) -Where is professor Pike?

- He is in his office. He is preparing for tommorow's lecture. Prof Pike always works at this time.

He prepares is a general habit. He is preparing means now.

7) While the children were sleeping, Miss Smith was cooking dinner.

Remember the article. Without it, you mean children in a general sense. Every child in the world?
8) We have seldom gone to the theater, because we have a lot of work.

General habits and facts: use present simple.
9) With whom is talking your husband talking?

Quite formal, but correct.
10) How do you spend your weekends day?
11) We always do a lot of spoken exercises in the class.
12) Ms. Piters is walking now. She likes walking at the in rainy weather.
13) I met Anna last week, but we didn't talk, because she had been hastening was running to the cinema.

Hasten is a farly old word. She had been hastening means she was not running, but instead was probably too tired to talk because she was running earlier. 
14) When I looked in the audience, students had written conrol work.

I really don't understand what you wanted to say.
15) Mr. Parker is on the vacation now.

The is not necessary. We know Mr Parker is enjoying a vacation, but we don't have or need specific details.
16) When we lived in Moscow, I had often went to the Hermitage.

When you use perfect tenses, that action happens before (and connects to) a later event. The events never happen at the same time.

grammar

1) When we came, the guests were dancing .
2) What is the matter? Why is the child crying?
3) -What are you looking for? - I am looking for the comb. I left it on the table yesterday, but it isn't there now.
4) I was sitting next to Mr.Lane on the bus yesterday. we were talking about work, about our plans for the future. Mr. Lane thinks he will spend summer in the mountains.
5) Henry seldom (rarely) writes letters to his parents, but he often rings them. 
6) -Where is professor Pike?- He is in his office. He's preparing for tomorrow's lecture. pfr. pike always works at this time.

Try to revise your grammar and correct the rest of your sentences yourself :)