The maps not showing is just about always because there is a bug in the theme or another plugin. If you share a link to your directory, I’ll take a look.
Currently no template for Connections supports searching/filtering by character. That feature will come later this summer. What it does support is jumping to the character clicked only if that character is on the current page of results. Hope that makes sense.
The CSS files for cMap can be found here:
Make you edits to the cmap.css file and then update the minified version; cmap.min.css. If you do not update the minified version, you will not see any changes you’ve made.