Hi @samiah.adams,
An advanced search would be a good option for you. I recommend that you conduct an advanced search for all tasks within the projects you speak of. Then, view the results in calendar view.
Regarding Google Calendar export, all projects do need to be synced individually. You can view all GCal / Asana functionality in this Guide article: Sync Asana + Google Calendar, Outlook, Apple | Product guide • Asana Product Guide
Best,
Alexis