The correct use of commas

Hello

I have a question regarding the correct use of commas.

In the following three sentences, is the single comma in the correct place? Is it possible to lose the comma? It would also be of great help to learn what the group of words following the comma are classed as, if not a dependent clause. All three sentences sound fine to me, but I just want to be sure.

1. I teamed them with a matching handbag and grey trouser suit, believing myself to be quite the sophisticated young woman.

2. A jazzy pulse begins, just drums and double bass.

3. Jenna reached her hand across the table, placing it on Dan’s arm.

Thank you