Thanks for your question and for including the full text of your shortcodes; very helpful.
You can replace your size_class parameter with size=full to get the larger image you want; more details on the size parameter are in the MLA Documentation tab.
You don’t say specifically what URL you need to get the author’s profile page. WordPress provides an “AUTHOR ARCHIVES” page, which I’ve used in the example below. You should be able to adapt that to your needs. If not, more details will let me give you more specific help.
Here is an updated version of your shortcode with solutions for your two problems:
[mla_gallery attachment_category='photo' columns=1 posts_per_page=12 size=full mla_caption='{+title+}<br><a href="https://projectdmc.org/support/topic/displaying-large-photo-and-author-name-with-link/{+site_url+}/author/{+author:user_nicename+}">{+author+}</a>']As you can see, the author name can be turned into any link you want. WordPress uses the user_nicename value for its author archives URL. This value is not available in the core MLA plugin but you can add it by installing one of the MLA Example plugins. To install the example plugin, navigate to the Settings/Media library Assistant Documentation tab and click the “Example Plugins” button. Type “author” in the text box and click “Search Plugins” to filter the table.
You are looking for the “MLA Substitution Parameter Hooks Example” plugin. Find that plugin and hover over the title in the left-most column. Click the “Install” rollover action, then go to the WordPress Plugins/Installed Plugins submenu and activate the example plugin as you would any other plugin. Once the example plugin is active you can access the {+author:user_nicename+} value or use the author: prefix to get any other “user” value for the item’s author.
I am marking this topic resolved, but please update it if you have problems or further questions regarding the above suggestions. If you need more specific help composing the author profile URL, any additional details or examples will be helpful. Thanks for your interest in the plugin.