See https://tedgustaf.com/blog/2016/display-thumbnail-for-image-properties-in-episerver/ for how you can extend the image property.

For adding a button next to the media button, you can do something like:

define([
    "dojo/_base/declare",
    "dojo/dom-style",
    "dojo/aspect",

    "epi-cms/widget/ContentSelector"
],

function (
    declare,
    domStyle,
    aspect,

    ContentSelector
) {
    return declare([ContentSelector], { 

		startup: function () {
			var button = new Button({ label: "Click me" });
			button.startup();
			button.placeAt(this.inputContainer);
			button.on("click", function(event) {
				event.preventDefault();

			var dialog = new Dialog({
				title: 'title of dialog',
				content: '<p>Text</p>'
			});

			dialog.show();

			}
		}

    });
});

Also check Marijas nice blog about extending dojo parts for link

http://www.mogul.com/om-mogul/blogg/extending-episerver-link-in-tinymce-to-support-anchors-on-page