1. He is rather an old man.

1-2. He is a rather old man.
(Are both OK and grammatical?)

2. She is quite a good pianist.
2-2. She is a quite good pianist.
(Are both OK and grammatical?)

3. I feel better than last night.
(What is the postive degree of 'better', good or well?)

4. They came home earlier than usual.
(What is the full form of this sentence? They came home earlier than they came home usual.--Is this the full form?)

5. Let's wash our hands for the meal.
5-1. Let's wash our hands for the next meal.
5-2. Let's wash our hands after the meal is ready.
5-3. Let's wash our hands after the meal is over.

(Are all the expressions grammatical?)

6. I have to get up at sunrise to catch the train.

6-1. I have to get up around sunrise to catch the train.

6-2. I have to get up at the sunrise to catch the train.

6-3. I have to get up around the sunrise to catch the train.

(Which expressions are correct? Do we have to use 'the' or not?)

7. He was rather angry, so she didn't want to have a seat next to her.
(Can we use 'a little', 'kind of',or 'somewhat' instead of 'rather' in this sentence?

1. He is rather an old man.

1-2. He is a rather old man.
(Are both OK and grammatical?)
Both are fine.

2. She is quite a good pianist.
2-2. She is a quite good pianist.
(Are both OK and grammatical?)
#2 is fine; 2-2 is not used.

3. I feel better than last night.
(What is the postive degree of 'better', good or well?)
In this case, "good." Without any comparison with something else, you'd say, "I feed good."

4. They came home earlier than usual.
(What is the full form of this sentence? They came home earlier than they came home usual.--Is this the full form?)
I'd say, "...earlier than [their] usual [time]." Otherwise, you'd have to be using "usually."

5. Let's wash our hands for the meal.
5-1. Let's wash our hands for the next meal.
5-2. Let's wash our hands after the meal is ready.
5-3. Let's wash our hands after the meal is over.

(Are all the expressions grammatical?)
All are fine.

6. I have to get up at sunrise to catch the train.

6-1. I have to get up around sunrise to catch the train.

6-2. I have to get up at the sunrise to catch the train.

6-3. I have to get up around the sunrise to catch the train.

(Which expressions are correct? Do we have to use 'the' or not?)
#s 6 and 6-1 are fine; the others are not used.

7. He was rather angry, so she didn't want to have a seat next to her.
(Can we use 'a little', 'kind of',or 'somewhat' instead of 'rather' in this sentence?
I think you mean "he" instead of "she," right? You can use all those variations, yes, but only "rather" and "somewhat" are grammatical; the other two are very informal. Technically, "a little" and "sort of" need to be followed by nouns, not adjectives.

I should have written this:

3. I feel better than last night.
(What is the postive degree of 'better', good or well?)
In this case, "good." Without any comparison with something else, you'd say, "I feel good."

Or, in #6, "he was rather angry, so she didn't want to have a seat next to HIM."

Sra

Ahhh, yes -- Sra is right.

1. Both sentences are grammatically correct, but they have slightly different meanings. In sentence 1, "rather" emphasizes the degree to which the man is old, suggesting that he is quite old. In sentence 1-2, "rather" modifies "old," indicating that the man is old to a certain extent, but perhaps not extremely old.

2. Both sentences are grammatically correct, but again, they convey different meanings. In sentence 2, "quite" stresses the level of skill the pianist possesses, suggesting that she is very good. In sentence 2-2, "quite" modifies "good," conveying that the pianist is good to a certain degree, but maybe not exceptionally good.

3. The positive degree of "better" is "good." In this context, "better" is a comparative degree as it compares the speaker's current state to their previous state. So, the positive degree would be "I feel good."

4. The full form of the sentence is "They came home earlier than they usually come home." The word "earlier" establishes a comparative relationship, and to complete the comparison, we need to specify what they are earlier than, which is "they usually come home."

5. All the expressions are grammatically correct and convey a similar meaning. They all suggest the action of washing hands in relation to the meal. However, the expressions slightly differ in their timing. 5-1 suggests washing hands specifically for the subsequent meal, 5-2 indicates washing hands once the meal is ready, and 5-3 implies washing hands once the meal is finished.

6. The correct expressions are 6 and 6-1. "I have to get up at sunrise to catch the train" and "I have to get up around sunrise to catch the train" are both acceptable. The use of "the" before "sunrise" is optional. Including "the" makes it more specific, referring to a particular sunrise, while omitting "the" makes it more general, referring to the concept of sunrise in general.

7. Yes, you can use "a little," "kind of," or "somewhat" instead of "rather" in that sentence. So the sentence can be rewritten as "He was a little angry, so she didn't want to have a seat next to him." The meaning and emphasis would slightly change with each replacement, but the sentence would still be grammatically correct.