Is it safe use wp_editor in public contact form

It should be fine and secure, as Horttcore mentioned it isn’t making any database or backend changes it is simply displaying the tinymce editor. There are other plugins you could use of course but I don’t see any problems doing exactly what you are doing.

To answer your other question, I believe the text/visual switch is stored in a cookie so only you would see this change and only if you switched it on the public form yourself – other people changing it on the public end won’t change your settings for text/visual on the backend.