If i forget to fill in one field, all fields I have already filled in get empty, I have to start all over

This is strange because we use also HTML5 client validation, so when you have not filled all data you should not go ahead. Maybe you have some javascript error. Can you please post me your site link to check this issue?

when saving the form it says my e-mail is already registered while I just try to update my profile with mandatory fields

Set all menu item of type User Manager->Registration Form to guest ACL. For more information read here https://www.easy-profile.com/support/404-when-user-updates-his-profile.html#reply-8835

Hi,

Only the password needs to be filled in again which is a bummer if you are in another tab for completion. Is there a way to have this remembered?

No sorry, this is not possible, password never stored.

And can people also enter a date of birth without the calendar?

No sorry. We plan to make in future option to change from calendar to select fields (day,month,year)

And as last question, is there a way to have all profile information including file uploads to be e-mailed to administrators

Not natively, but you can write a simple plugin to do this, in our forum there are many examples, try to read here https://www.easy-profile.com/support/display-value-of-custom-fields-to-sent-emails.html#reply-8818
You can improve our example to attach file to email, or most simple you can send only document link (user value contain relative link to file)