Thank you for writing in, please set your column's text-align option to center, and this will center the elements inside it.
The search box you have on the bottom of the page is the Search Inline element, please inspect that element and style it, the magnifying glass that its there is actually the submit button, you can style it.
However, the search box you have above on that page seems to be a 3rd party widgets. You can duplicate that Classic RAW element instead and drag it on the bottom replacing your current search box in there.
Regarding the search result page, the only way to edit the search result page is through template customization. You can't edit it through the builder since it's Wordpress generated page. It's true in every theme, you may find more information here https://codex.wordpress.org/Creating_a_Search_Page. But that's just a general knowledge to create search templates.
And redirection may not work since it's static, and search URL could vary. You may consult it with a developer to have a fully functioning custom search result.
Thanks for understanding.