I got "message Your theme’s template file single.php for displaying Application items is missing custom fields" from Toolset Dashboard. What does it mean? How can I fix it? Could you show me some examples?
It just means that your theme's PHP template that will be used to display single Application posts won't output and custom fields assigned to your Application posts.
You can create a Content Template (at Toolset > Content Templates) to customize what is output in the content area of your single Application posts, and you can add whatever fields you want to that template.
Is it a must to have the content template for each custom post type? What can I do if I do want the custom post type be shown by default, or it shows a 404 page?
It is not s must-have, it depends on what you want from the template of the custom post type.
By default, if you do not add a content template, whatever custom post type you create will show your theme's single.php file.
SO you can test, you can add the custom post type and add a few posts of that type and click the PREVIEW link to see what info the theme shows.
If it is enough and ok with you, then you can avoid adding a content template. But if you also have other custom fields assigned to that custom post type that you want to show in the front end and the theme default does not show it, you should create a content template and decide which info you want to add.
The content template will override the theme default if you assign the content template to the custom post type in question.
I suggest that you read the link my colleague shared for more detailed information about content templates.
