Problem:

How to add search and filter to a view table.

Solution:

- You can use block editor and add a table view

- You can add search in the table view

- You can change the type of the input for the search to dropdown or checkbox

Check this video:

https://www.loom.com/share/de3ffe51dfba4adfa4044b703a7e8396

Problem:
How to have dropdowns for custom taxonomy (custom post type category) by default

Solution:
To display the taxonomy as drop-down select box you can use the following shortcode:

You can find the proposed solution in this case with the following reply:
https://toolset.com/forums/topic/how-to-have-dropdowns-for-custom-taxonomy-custom-post-type-category-by-default/#post-2364465

Relevant Documentation:

Problem:
How to group posts by month

Solution:
If you want to group posts by month using the custom date field, you will have to use the custom shortcode.

You can find the proposed solution in this case with the following reply:
=> https://toolset.com/forums/topic/group-results-by-year-and-month-using-date-field/

Relevant Documentation:
=> https://toolset.com/2013/10/how-to-group-views-results-by-year-and-month/