Can we create our own theme’s function.php?

You can, and should, make your own functions.php file.

You can’t drop a whole chunk of code that depends on other files into your theme and just expect it to work. It probably also contains a load of things you don’t need.

Start with an empty functions.php and just add things as you need them. Have a look at the sorts of functions used in one of the themes by wordpress.org or Automattic as a good starting point, as they tend to be pretty clean compared to some other themes and also try to showcase the newest theme features. Twenty Sixteen maybe.