Should I fetch the data managed by a plugin by using its APIs or WordPress APIs?

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I’ll answer myself after having completed my two points in the last few days of work:

  1. My plugin, which indeed did all of the data insertion and management work, contained some very handy APIs in its codebase. WordPress does also provide some very great database access APIs (amongst other things) and I can say that I used them interchangeably. In general, I gave priority over the plugin functions, but if I didn’t find a useful API it was easy constructing one myself on top of WordPress’. However, I never used direct MySQL queries, like through the wpdb class.

  2. I also needed to define templates for single menu items, which actually were posts. In the only one case so far, I created a single-mp_menu_item.php template file within my child theme directory, and I modified code pasted there from the parent theme to suit my needs. What is important to note though, is that I did not resort to using action and filter hooks as recommended by the plugin documentation.