Add field 'link' in a block form?
You should add the field from the Block Type interface. Either add to the block type that comes with core or create a new one and add your fields.

Also, no, Drupal Fields and Form API elements are two different constructs. That is why 'link' does nothing. It would simply be:

$form['key_2'] = [
    '#title' =&gt; $this-&gt;t('key 2 link'),
    '#type' =&gt; 'url',
];


See: https://api.drupal.org/api/drupal/core%21lib%21Drupal%21Core%21Render%21Element%21Url.php/class/Url/8.2.x

But you're creating more work that necessary.

In this context (a form) link pertains to a RenderElement and not a FormElement like url is.