1. She held out her hand.

2. She extended her hand.
---------
Are both the same? Can we use some other expressions instead of 'held out'?

3. It's been such a long time.
4. It's been so lone a time.
---------------------------
What does 'It' refer to here?
Is #4 correct?

5. He raised his right hand a little.
6. he raised his right hand much.
7. He raised his right hand just a bit.
8. He raised his right hand high.
9. He raised his right hand in middle position.
10. He raised his right hand next to the top of his head.
------------------------------
Are they all grammatical from 5 to 10?

1, 2, 3, 5, 7, 8, and 10 are all fine. The others are not used.

It = impersonal reference.

1. "She held out her hand." and 2. "She extended her hand." convey a similar meaning, as both phrases describe the action of offering one's hand to someone else. However, there are some slight differences in connotation.

"Held out" suggests that the hand is being held forward or offered, indicating a physical gesture of reaching out. It implies an action of offering or presenting the hand to someone.

"Extended" simply means to stretch out, so "She extended her hand" can refer to physically stretching out the hand, but it may not necessarily imply offering it to someone.

Alternative expressions that can be used instead of "held out" are "reached out" or "stretched out." Both phrases convey the idea of extending or offering the hand.

Regarding your second question:

3. "It's been such a long time" is a complete sentence with "it" as a pronoun. In this sentence, "it" is used as a placeholder or subject to refer to an event or period of time.

4. "It's been so lone a time" seems to be an error in phrasing. The correct way to express the same idea would be "It's been such a long time."

Moving on to your third question:

From 5 to 10, all the sentences are grammatically correct, but there are some differences in phrasing and meaning.

5. "He raised his right hand a little" indicates a slight elevation of the hand, suggesting a small movement upward.

6. "He raised his right hand much" is not commonly used. A more natural alternative could be "He raised his right hand significantly" or "He raised his right hand a lot."

7. "He raised his right hand just a bit" means a small or minimal movement upward, similar to sentence 5. In this case, "just a bit" emphasizes the small degree of elevation.

8. "He raised his right hand high" suggests a significant elevation of the hand, indicating a noticeable or considerable movement upward.

9. "He raised his right hand in the middle position" is grammatically correct, but the intended meaning is not clear. If you mean the hand is elevated to a midpoint position between low and high, then you could rephrase it as "He raised his right hand to a mid-position."

10. "He raised his right hand next to the top of his head" conveys the idea of raising the hand close to the uppermost part of the head. However, this sentence sounds somewhat awkward. A better alternative would be "He raised his right hand near the top of his head."

Remember, while the sentences may be grammatically correct, it's important to consider the context and intended meaning to choose the most appropriate phrasing.