Hi,
sorry for late reply, now it's night for us and our offices are closed.

you can use our built in Joomla Contact integration, if you have a contact (from Administration->Components->Contacts, see screenshots) linked to some user you will see "Email" button on the profile page, this button link to contact page.

You can also create automatically contact when user register an account, to do this you can enable a plugin called "User - Contact Creator". This plugin is available in all Joomla installations and disabled by default

Example on this site: now I have created a Joomla contact linked to my account, so at https://www.easy-profile.com/profile/admin.html you will email button to contact me

Thank you, so far it works.

Is there a way to auto display a contact form on every profile without having to click the e-mail button?

Hi,
sorry Easy Profile do not do this. You need to develop a module or plugin, but this is not simple.