Drupal views get field info from node within another field
I assume that you are using the References module to provide a Node Reference field to Photo Gallery nodes which reference Projects, and then provide another Node Reference field, or Term Reference field to Project nodes which reference Categories?

In Views:


Expand the Advanced column
Add a Relationship
In the Add Relationships dialog, select the Photo Gallery: Project Node Reference field from the list
In the Configure Relationship dialog, Click Apply
Add another Relationship
This time in the Add Relationships dialog, select the Project: Category Node/Term Reference field from the list.
In the Configure Relationship dialog, there is a field labelled Relationship with a drop-down menu, which lets you choose other compatible relationships you've added previously, from which you should select the Photo Gallery: Project relationship (I'm not entirely certain what text to expect here). Then click Apply.
Now when you add new Fields to the View, you'll have the option to select a Relationship for each individual field, which allows you to pull data from the entity (Node/Term) that is referenced by the selected Relationship