Sure, here are the answers with brief explanations:

1. **Hardly had they been** there 5 minutes when Mrs. Brown **came** in with the coffee.
- "Hardly" is used with past perfect ("had been") and simple past ("came") in the main clause.

2. **Scarcely had they moved** into the new house when their friends **came** in.
- "Scarcely" is used with past perfect ("had moved") and simple past ("came") in the main clause.

3. **I had met** John before I **had been** a fortnight in Paris.
- Past perfect ("had met") for the action that happened before the other past action ("had been").

4. **He had no sooner reached** the door than he **came** back.
- "No sooner" is used with past perfect ("had reached") and simple past ("came") in the main clause.

5. **He had** a bad fall while he **was repairing** his roof.
- Past simple ("had") and past continuous ("was repairing") for an ongoing action interrupted by another past action.

6. **By the end of this month, I hope, I will have written** 200 pages of my new novel.
- Future perfect ("will have written") for an action that will be completed by a specific time in the future.

7. **It took** a moment before Nick **realized** he **had been offered** a cigarette by the stranger.
- Past simple ("took", "realized") and past perfect passive ("had been offered").

8. **While he was learning** to drive he **had had** 25 accidents.
- Past continuous ("was learning") and past perfect ("had had") for repeated actions in the past.

9. **It’s no use getting** impatient. The plane **won't arrive** until the weather **clears** up.
- Present participle ("getting"), future simple ("won't arrive"), and present simple ("clears").

10. **I have been thinking** about you a lot lately and I **have come** to the conclusion that I **won't be** able to live without you.
- Present perfect continuous ("have been thinking"), present perfect ("have come"), and future simple ("won't be").

11. **I don’t mind waiting. I’d rather be** too early than too late.
- Gerund ("waiting") and base form after "would rather" ("be").

12. **Those students who failed** the exam are going to take another one held in August.
- Past simple ("failed") for a completed action in the past.

13. **“I am just going out to get an evening paper.” “But it is raining. Why don't you wait** till the rain **stops**?”
- Present continuous ("is raining"), present simple ("don't wait"), and present simple ("stops").

14. **I think** your father’s health **has improved** so much since I **saw** him last.
- Present simple ("think"), present perfect ("has improved"), and past simple ("saw").

Sure, here are the answers with brief explanations:

1. **Hardly had they been** there 5 minutes when Mrs. Brown **came** in with the coffee.
- "Hardly" is used with past perfect ("had been") and simple past ("came") in the main clause.

2. **Scarcely had they moved** into the new house when their friends **came** in.
- "Scarcely" is used with past perfect ("had moved") and simple past ("came") in the main clause.

3. **I had met** John before I **had been** a fortnight in Paris.
- Past perfect ("had met") for the action that happened before the other past action ("had been").

4. **He had no sooner reached** the door than he **came** back.
- "No sooner" is used with past perfect ("had reached") and simple past ("came") in the main clause.

5. **He had** a bad fall while he **was repairing** his roof.
- Past simple ("had") and past continuous ("was repairing") for an ongoing action interrupted by another past action.

6. **By the end of this month, I hope, I will have written** 200 pages of my new novel.
- Future perfect ("will have written") for an action that will be completed by a specific time in the future.

7. **It took** a moment before Nick **realized** he **had been offered** a cigarette by the stranger.
- Past simple ("took", "realized") and past perfect passive ("had been offered").

8. **While he was learning** to drive he **had had** 25 accidents.
- Past continuous ("was learning") and past perfect ("had had") for repeated actions in the past.

9. **It’s no use getting** impatient. The plane **won't arrive** until the weather **clears** up.
- Present participle ("getting"), future simple ("won't arrive"), and present simple ("clears").

10. **I have been thinking** about you a lot lately and I **have come** to the conclusion that I **won't be** able to live without you.
- Present perfect continuous ("have been thinking"), present perfect ("have come"), and future simple ("won't be").

11. **I don’t mind waiting. I’d rather be** too early than too late.
- Gerund ("waiting") and base form after "would rather" ("be").

12. **Those students who failed** the exam are going to take another one held in August.
- Past simple ("failed") for a completed action in the past.

13. **“I am just going out to get an evening paper.” “But it is raining. Why don't you wait** till the rain **stops**?”
- Present continuous ("is raining"), present simple ("don't wait"), and present simple ("stops").

14. **I think** your father’s health **has improved** so much since I **saw** him last.
- Present simple ("think"), present perfect ("has improved"), and past simple ("saw").