1. How can I allow users to add titles/captions/descriptions to their images they uploaded with a frontend form
If you use the Media Uploader, which is also avaialbe in CRED, you can do it as I elaborated earlier.
If you use a Custom Field, then you can use either a Custom Field (single line as example), and use that later for the display, or, you can use Custom Code and hook it to the CRED API hook cred_save_data():
https://toolset.com/documentation/programmer-reference/cred-api/#cred_save_data
2. But unfortunately, they do no work within Views Content Templates when search and filtering are applied
This is most likely because you use AJAX filters.
When you use AJAX you need to fire your Custom JS again, and that can be done by calling the custom functions in the JS Front-End events of Toolset.
Those are listed in the Custom Search JS Section, when you press the Button "Front-End JS events".
This will automatically hook your functions to the correct Views Hooks you will choose.
The Custom functions are of course subject to custom code/libraries.
3. I recently tried adding ACF custom fields to my Types created custom post type, but the Types CPT did not appear in the "Manage non-Toolset Post Fields" menu options.
Yes, because the Types CPT will not appear on that screen.
What appears there, are Fields of 3rd Parties.
When you create CPT's with Types, the idea is to create Custom Fields with Types as well.
That screen is used to control 3rd Party Fields, not types fields.
You could circumnavigate that issue by assigning your ACF Fields to any other Post type as well.
This seems a little usability issue as well, IMHO, there should be queried only Fields of non-Types type, and not CPT's.
I will eventually report that if I can replicate it.
It should be more like in Toolset > Post Fields > Post Field Control
This is a new feature, in case it gets accepted, and as such, I would then file it.