Sure! Here are the filled-in blanks along with explanations for each one:

1. Nam is very happy **to help** his grandfather with **planting** roses in the garden.
- "to help" is the infinitive form of the verb following "happy." After the phrase "happy to," we use the infinitive form. "planting" is the gerund form of the verb that follows "with."

2. He says he detests **reading** science fiction.
- "reading" is the gerund form of the verb, which is used after the verb "detests."

3. Listen to this! I think this news **will surprise** you.
- "will surprise" is the future simple tense used here to express a prediction about the news.

4. The statue **broke** while it **was being moved** to another room in the museum.
- "broke" is the simple past tense of the verb "break," indicating the action happened in the past. "was being moved" is the past continuous passive voice, indicating the action was in progress when the statue broke.

5. People used **to make** fire by **rubbing** two sticks together.
- "to make" is the infinitive form used after "used." "rubbing" is the gerund form describing the action that follows "by."

6. It is our fault to keep Alice **waiting** so long. We **should have informed** her in advance.
- "waiting" is the gerund form used after "keep." "should have informed" is the modal perfect form used to express regret or a missed obligation in the past.

So, the completed sentences are:

1. Nam is very happy **to help** his grandfather with **planting** roses in the garden.
2. He says he detests **reading** science fiction.
3. Listen to this! I think this news **will surprise** you.
4. The statue **broke** while it **was being moved** to another room in the museum.
5. People used **to make** fire by **rubbing** two sticks together.
6. It is our fault to keep Alice **waiting** so long. We **should have informed** her in advance.