I've looked on the CB website but cannot find a simple listing of the features of Community Builder—there certainly are long descriptions but they don't really go into much detail. Is there one published somewhere?

Core CB functionality can be found below.

www.joomlapolis.com/community-builder

We however have a significant amount of addons that can give all kinds of new functionality that you can check out below.

www.joomlapolis.com/addons

Easiest way to see what is available is to just start tinkering with our demo site below (feel free to change anything you have access to).

demo.cbdemosites.com/

• Can we csv Import member data?
• Can we csv Export member data?

With 3rd party plugin CB Juice, yes.

• Can we mass email members?

Yes, from CB > User Management.

• Can we control what fields are displayed in Search results?

Yes, from CB > Field Management.

• Any CRM Integrations?

No, but probably doable with CB Auto Actions.

• Can we create our own template/styling?

Yes, all our plugins are template driven as well as CB. However, CB is Bootstrap 3 and will soon be Bootstrap 4. So you could mass-style CB simply by using a Bootstrap driven Joomla template and turning CBs Bootstrap off in CB > Configuration > Integrations.

• Can the user search/filter by category, alphabetical, etc.?

There are no categories for profiles so unsure what you're referring to.

• Does a keyword search search all fields in a member profile?

If using Joomla search module and CB Search Bot, yes it'll search whatever fields you select it to search in the plugins parameters.