1. Walking in the park, I saw Mina.

2. When I walked in the park, I saw Mina.
3. When I was walking in the park, I saw Mina.

(Does #1 mean #2 or #3? Are they all the same?)

3-1. Being walking in the park, I saw Mina.(Is this one correct?)

4. With night coming on, we started for home.

5. Because night came on, we started for home.

(Does #4 mean #5?)

1, 2, and 3 are all correct and mean the same thing.

3-1 is incorrect.

4 has what's called a "dangling" or misplaced modifier; it's incorrect.

5 is correct.

Essentially they mean the same thing, but grammatically you should never start a sentence with the word because. Instead try using; as a result..., this caused..., or even the reasoning for this/ that is...

1. "Walking in the park, I saw Mina" suggests that the person was already walking in the park when they saw Mina. It does not provide any information about the duration of the walk or whether it was a specific occasion. It is a simple statement of the fact that they saw Mina while walking in the park.

2. "When I walked in the park, I saw Mina" indicates that the person saw Mina during a specific instance of walking in the park. It suggests a singular occurrence of walking, possibly implying that they don't walk in the park regularly.

3. "When I was walking in the park, I saw Mina" implies that the person saw Mina while they were in the middle of the action of walking in the park. It emphasizes the ongoing nature of the activity.

In summary, #1 suggests a general statement, #2 implies a specific instance, and #3 emphasizes the ongoing action of walking.

3-1. "Being walking in the park, I saw Mina" does not follow standard English language rules. The correct phrasing would be "While I was walking in the park, I saw Mina."

4. "With night coming on, we started for home" implies that the group decided to begin their journey home as the night was approaching. It suggests that the impending darkness was a factor in their decision.

5. "Because night came on, we started for home" indicates that the group started their journey due to the arrival of night. It suggests that the change from daylight to darkness was the reason for their action.

In summary, while both sentences convey the idea that the group started for home due to the approaching night, #4 focuses more on the gradual transition of night coming on, whereas #5 highlights the cause-effect relationship between the arrival of night and the decision to start for home.