In the reports section, I see that I can change and adjust default reports. Is there a way for me to build a report entirely from scratch?
Via the UI, you'll need to create reports using one of the templates available (e.g., from /civicrm/report/template/list?reset=1 ). If you have coding experience, you can create custom reports from scratch, yes. Here is the report reference from the Civi wiki: https://wiki.civicrm.org/confluence/display/CRMDOC/CiviReport+Reference
Yes, you can make a CiviCRM Extension. Within that extension you can make a (or more) custom report(s).
For more info about creating the extension: https://wiki.civicrm.org/confluence/display/CRMDOC/Create+an+Extension
For more info about creating the report within the extension: https://wiki.civicrm.org/confluence/display/CRMDOC/Create+a+Module+Extension#CreateaModuleExtension-Addareport
I never start from scratch! I always look for a core report that mostly closely resembles what I need to do - then I clone that and start from there to add in my fields (columns), my filters, group by, from, display alter etc.