Display an image search api page result
You first have to add the image to the index. Then preferably reindex.
Usually for some reason the image fields are hidden on the page, where you add the fields to the index.
The page in Drupal 7 would be under Search and metadata > Search API > Your index, edit > Fields
/admin/config/search/search_api/index/NAME_OF_INDEX/fields

And your image field you may add from the bottom - the section is called "Add related fields" and then you should choose your field and click "Add field". Afterwards you may click the checkbox to the field - in order to add it to the index.

The approach with node_load is a very bad one because that would load stuff from the database, where the idea of Search Api and in this case the connection with Apache Solr - is to get everything directly from the Solr.