Getting user photo url and profile url using views_json
To get the user pic url, you can do it using Image URL Formatter. Once enabled, when you click on the user picture field, you will now see a formatter option, select image url.

For the user, assuming this is a user view, in FIELDS add the User: Uid as a field and checkmark ☑ exclude from display.

Now, add Global: Custom text as a field. In the text box, put http://ultrabob.com/user/[uid]

I got [uid] from replacement patterns. Side note, in order for fields to appear as a replacement pattern, they must be above the current field.

Else, if you're using pathauto so the user pages are /user/[username] then add the User: Name field instead and use the [name] token.

Now, if your view is a content view, ex: shows articles, then you will need to add a relationship of node author first, once you do that, the user fields will become available to be added as a field. 




  OK, that issue got me sorted with the pictures, I'm now working on the
  solution for profile page link. Can you think of a good way to get the
  domain part of the url (http://ultrabob.com/) in your example
  dynamically in views from the site configuration. I would like this to
  continue to work without modification as it is deployed across test
  servers and onto production


You can using php. Ex: &lt;?php echo $_SERVER['HTTP_HOST']; ?&gt;

Either you could enable the Views PHP module, but remember to turn it off on production, or use a template file. 

views-view-field--[view-name]--views-data-export--[field-name].tpl.php

&lt;?php

$fields["field_name"]-&gt;content = 'http://' . $_SERVER['HTTP_HOST'] . '/user/' . $fields["field_name"]-&gt;content;

echo $fields["field_name"]-&gt;content;