Problem:

The issue here is that the user wanted to edit a single custom field on their posts in a list without going to the post page itself.

Solution:
To resolve this you can create an edit post form and set it to submit using AJAX. Then removed all the fields that aren't needed leaving only the needed field and the submit button.

Finally just add that form to the view listing out your posts. From there you can Edit the Field A and change the values for each of the posts without having to go to the post itself. You can edit the fields from the list.

Problem:

The issue here is that the user is getting the error "Toolset plugin cannot connect to toolset"
Solution:
To resolve this. try going to your wordpress backend and click Dashboard -> Updates and then hit Check Again.

Problem:
Add Toolset Hook to my custom plugin

Solution:
The setting for admin bar option is saved within the wp_options table with the key "toolset_options" where we save the settings as serialized array.

You just need to get the value of key "toolset_options" from wp_options table and then unserialize it and look for the array key "show_admin_bar_shortcut" which holds the value either "on" or "off".

If you want to display the "Design with Toolset" menu, you should update the "show_admin_bar_shortcut" to "on" and if you want to disable it then set it value to "off" and accordingly save the "toolset_options" key value.

Relevant Documentation: