In JA Alumni its different style and js used, for this you need to do customization in the php file, css and js.
You can try this too.
Open JA Alumni script.js file to copy the js .
Now to apply the same css style on this template use firebug or inspect element.
Also, you need to add has-slideshow as page class so the css will work,
Let me explain it:
When the menu is fixed it will hide the content.
So in mobile, you changed padding values that make it upper.
This needs more style to give it different style for different screen sizes.
In JA Alumni header, you can open the header.php file to see the menu
script.js file for sticky menu js code
template.css file contains the style code for the sticky header and style for topbar
and /tpls/default.php file to see the bodyclass code
For the other changes, it needs to define the new style code in custom.css because change the default style in the template will affect other parts, for example, the sticky will hide the content a little.