Hi,
I would like to customize it to have a shorter height and length.
It’s height should also be affected when you change the secondary navigation’s Menu Item Height on Appearance > Customize > Layout > Secondary Navigation.
But if you want to keep the second nav’s height and only change the search’s width and height, you’ll have to do it with custom CSS.
Since I would also like to have my social icons to the left of my search bar, do I need to create a custom top bar using hooks in elements?
How did you insert the search bar? did you use this? https://docs.generatepress.com/article/navigation-search/
If so, you can use the same hook. Just make sure the search bar has higher priority so it appears before the search icon.