*1). My sister touched the pot. She did not realize that it was hot.*

<Reduced> 1a). Touching the pot, she did not realize that it was hot.

<Reduced> 1b). My sister touched the pot, not realizing that it was hot.

2). We walked up and down the room. We tried to find a way to solve our problem.

<Reduced> 2a). Walking up and down the room, we tried to find a way to solve our problem.

<Reduced> 2b). We walked up and down the room, trying to find a way to solve our problem.

3). The driver lost control of his car. He hit a cyclist and smashed into a shop window.

<Reduced> 3a) Losing control of his car, he hit a cyclist and smashed into a shop window.

<Reduced> 3b) The driver lost control of his car, hitting a cyclist and smashed into a shop window.

<Reduced> 1a). Touching the pot, she did not realize that it was hot.

<Reduced> 1b). My sister touched the pot, not realizing that it was hot.

2). We walked up and down the room. We tried to find a way to solve our problem.

<Reduced> 2a). Walking up and down the room, we tried to find a way to solve our problem.

<Reduced> 2b). We walked up and down the room, trying to find a way to solve our problem.

3). The driver lost control of his car. He hit a cyclist and smashed into a shop window.

<Reduced> 3a) Losing control of his car, he hit a cyclist and smashed into a shop window.

<Reduced> 3b) The driver lost control of his car, hitting a cyclist and smashed into a shop window.

Do the above sentences (a and b) have any differences in meaning between them?

By the way, are all the above sentences (a and b) written correctly (in term of grammar)?

Thank you.