We are very happy to know that you are using child theme for theme customization. You are doing absolutely right way.
It seems like you have already started to customize. You have added this code.
which is good.
Now you have to change the logo( image ) size. Currently your logo size is 290 * 60, please increase logo size.
Further if you are willing to change file for the header, the file is not core.php, it is header.php inside acmethemes/hooks/header.php of theme folder supermagpro. You can just copy paste file in the child theme in the same path eg. in child theme create acmethemes folder then inside there create hooks folder then paste header.php of parent theme there, now you are good to go for customization. Same goes on other files too.
If you have further query please feel free to ask.