There is some problem with your server configuration because AJAX requests in the Dashboard area returns 404 error https://gyazo.com/5f64028e5e3cba671fae55fc6e855736
Try to contact your hosting providers for help. It is not a problem with Theme Settings only. Widgets save function doesn’t work as well for example.
No, your website is not working now. Try to remove your plugins folder that you recently activated via FTP or your hosting panel file manager. Then reinstall these plugins.
The white screen says about some PHP error but we can’t identify it. You need to contact your hosting provider and ask to check what error appears there.