With regards to the prefixes (-webit-, -moz-), a ‘hack’ in Pinegrow is to convert your CSS to SaSS and then your compiled CSS will contain relevant prefixes (Page > Manage Stylesheets > Use SCSS/Less).
Having said that, appearance is not available in the visual editor. You will need to add this yourself by manually writing the code. Same goes with outline.
border: none; is achieved in the editor by filling out all of the border properties and Pinegrow will combine the top, left, bottom and right border to an abbreviated version. border: 0px none #000000. Having selected the style as none will give you your border: none. You can shortcut this by filling out just one border side and selecting the little = button to duplicate this property to all the other border properties.
Once again, having said that, you may as well just type border: none; manually.
Not sure if the line of ==== is an addition to your post? but these are all simple to find (however a search box in the visual editor would be great @matjaz )