Problem:

Do you know how I could dynamically fetch a custom taxonomy field that I will call "archive-center" in a category of posts?

Solution:

Please try to display the taxonomy field
shortcode directly, make sure it outputs the correct address values, for example:

[types termmeta="archive-center"][/types]

Relevant Documentation:

Problem:

How to save Forms Generic field value into database?

Solution:

Shortcode [cred_generic_field] does not save the value into database by default, please try to add parameter "persist" into it, and test again, for example:

https://toolset.com/forums/topic/use-fooevents-custom-field-in-form/#post-2330609

Relevant Documentation: