Hello
Q1) Can you display multiple custom post types on the same map?
Yes, you can select multiple custom post types in view block, so you can query posts of multiple custom post types.
See our document
https://toolset.com/course-lesson/creating-a-view/
Q2) Can each custom post type have its own marker icon?
Yes, you can display different marker icon for each post type, for example, you can use shortcode [wpv-conditional] to check the current post's post type value, and display different map marker, like this:
[wpv-conditional if="('[wpv-post-type]' eq 'cpt1')"]
Map Marker 1 shortcode here...
[/wpv-conditional]
[wpv-conditional if="('[wpv-post-type]' eq 'cpt2')"]
Map Marker 2 shortcode here...
[/wpv-conditional]
More helps:
https://toolset.com/documentation/user-guides/views-shortcodes/#wpv-conditional
https://toolset.com/documentation/programmer-reference/maps/maps-shortcodes/#wpv-map-render
Q3) I'm not seeing a multi-select in the custom field types? That seems like a huge gap in the offering if not.
Toolset Types plugin support custom checkboxes field, you can setup multiple choice options in it, see our document:
https://toolset.com/course-lesson/creating-custom-fields/
Q4) I want to allow users on the front end to edit their listing.
You can follow our document to setup the post form for editing post:
https://toolset.com/course-lesson/front-end-forms-for-editing-content/
And you can custom repeating field(same field slug, multiple instances) into field group
And you can send the emails with Toolset Forms, see our document:
https://toolset.com/course-lesson/send-notifications-when-someone-submits-the-form/
Q5) Can you search in multiple custom post types at the same time with search filters?
Yes, you can query multiple post types in one post view, and you can setup custom search form into post view, see our document:
https://toolset.com/course-lesson/creating-a-custom-search/
