1. An old man is walking away with a golden apple in his hand. He is holding the golden apple up high.
2. He is walking away with a golden apple up in his hand.
3. He is walking away with a golden apple up high in his hand.
[Can #1 be combined into #2 or #3?]
4. He is walking with his hair up.
5. He is running with both hands up.
6. He is sitting with his right hand up towards the roof.
7. He is sleeping with his right leg up on the chair.
[What about these sentences? Are they grammatical with 'up'?]
#3 is not clear. Is there a high and a low to one's hand, his hand? One can hold an apple up high (as opposed to at your waist), or hold your hand up high (above your head, shoulder height, etc.), but how can you hold something either high or low IN YOUR HAND?
1 and 2 both make sense.
Let's break down each sentence to determine if they can be combined or if they are grammatical with 'up'.
1. An old man is walking away with a golden apple in his hand. He is holding the golden apple up high.
This sentence describes an old man walking with a golden apple, and he is holding it up high. Since the verb "holding" is used, it implies that he is actively keeping the apple up high.
2. He is walking away with a golden apple up in his hand.
This sentence conveys the same general idea as the first sentence but uses a different phrasing. Instead of "holding the golden apple up high," it states "up in his hand." Although the meaning is similar, it is a slightly different expression.
3. He is walking away with a golden apple up high in his hand.
This sentence combines the phrasing of the first two sentences. It states that the old man is walking away with a golden apple in his hand, and that hand is held up high. So, yes, sentence #1 can be combined into #3.
Now let's analyze sentences #4 through #7:
4. He is walking with his hair up.
This sentence is grammatically correct. It states that someone is walking with their hair raised or styled in an upward direction.
5. He is running with both hands up.
This sentence is also grammatically correct. It states that someone is running while raising both hands upward.
6. He is sitting with his right hand up towards the roof.
This sentence is grammatically correct. It describes someone sitting and raising their right hand toward the roof.
7. He is sleeping with his right leg up on the chair.
This sentence is grammatically correct as well. It describes someone sleeping while resting their right leg on the chair.
Therefore, all the sentences you provided are grammatically correct and use "up" appropriately in their context.