Thanks for reaching out—happy to help shine some more light on your options.
First, regarding #1 (Client should not be able to see other participants), please note that this is not possible to remove with Zoom Meetings. If you don’t want participants to be able to see each other, we typically recommend leveraging webinars for this.
In regards to #2 (Phone Call option is not necessary), in addition to passing this in the init object, you will need to adjust this in the meeting’s settings as well. You can update a meeting’s settings programmatically using Update Meeting API. You’ll need to set audio to VOIP only.
As for hiding the participants button, there is no built in way to hide the participants button. However, you can hide it using your own JavaScript or CSS.