Sure! Here are the completed sentences with the correct verb tenses, along with explanations:

1. I **have not seen** your brother recently.
- (Present Perfect) Used to express that something has not happened at any time up to now.

2. They **have not contacted** each other for a long time.
- (Present Perfect) Indicates an action that has not occurred during a period up to now.

3. How long **have you studied** English?
- (Present Perfect) To ask about the duration of an action that started in the past and is still ongoing or relevant to the present.

4. How many times **have you seen** him since he went to Edinburgh?
- (Present Perfect) Used to inquire about the number of times an action has occurred up to the present.

5. Who is that woman? I **have never seen** her before.
- (Present Perfect) Expresses that at no point in the speaker's life has the action occurred.

6. We **are** from France. We **have been** there for 20 years.
- (Present Simple) Used for a general fact, while (Present Perfect) is used to describe the duration of the state.

7. I **have seen** that film several times because I like it.
- (Present Perfect) Indicates an experience up to the present.

8. Mary **has lost** her hat for 2 days.
- (Present Perfect) Although "for" is generally used with a duration that continues up to now, it might be more typical to say, "Mary **lost** her hat 2 days ago" if referring to a specific past incident.

9. He **has not finished** doing it yet.
- (Present Perfect Negative) This shows that the action is still unfinished up to now.

10. He **has not seen** him since Christmas.
- (Present Perfect Negative) Indicates an action that has not occurred during the time frame starting at Christmas up to now.

**Summary of Tenses Used**:
- **Present Perfect** is primarily used in these sentences to indicate actions that relate to the present, while **Present Simple** is used for general truths.