Thanks for writing in!
First step would be to create the pages. After that in button URL section add the absolute URL of the relevant pages to link buttons to the pages. I think I replied to similar question in following ticket you created. Please take a look:
Please make sure that you have added relevant link to the buttons. So button that's supposed to link to contact page should have contact page URL.
Looks like handwash page is not published. Can you please share the URL so I can take a look? If you would like to change the layout then under Pages > All Pages open the page in WordPress editor. Then click on the Settings icon and under Page Attributes > Templates select the template as per your requirement.
If those pages are created and edited in WordPress editor and if you would like to use Cornerstone then you will have to create the layout again in Cornerstone. If you haven't used WordPress editor then you can use Cornerstone editor freely without any issues.
X Theme comes bundled with Gallery plugins that you can take a look. You can use Envira Gallery plugin and can be installed from X > Validation > Extensions. To get started with Envira Gallery, please refer following post: