So you are building a custom theme and the plugins are not working properly on the theme you created.
Contact Form 7, I also have that on few of my websites.
I’m moving towards your custom theme causing the issue.
It’s a javascript error.
I am using the plugin now, it work fine even the upgrade works.
There has be a plugin or something that is interfering with your drag and drop.
It’s a looks fine on the browsers. The images do appear. Have you date the new wordpress platform? If so, then the update you make screw the some things. It’s best to reinstall the platform