1. Is there a search module that can display in a module position the CB search for fields?

Nope.

2. I would like to display the count of members in a list in a group of lists is it possible? Hope the image below will help

Nope.

You really need a custom search to fit your needs. CB just can't do what you're wanting. I highly suggest using a directory extension, which can provide exactly what you need with zero additional work or custom coding.

For example our directory below uses MosTree (it can be of course adjusted further).

www.joomlapolis.com/cb-solutions/directory

More directory extensions can be found below.

extensions.joomla.org/extensions/directory-a-documentation/directory