can Office 365 F1 mailbox access a regular Shared Mailbox?

Yes, but only via OWA

"An F1 user cannot add delegates to their own mailbox, but they can access another mailbox (including shared mailboxes) and perform any actions which have been delegated to them."
https://docs.microsoft.com/en-us/office365/servicedescriptions/exchange-online-service-description/exchange-online-service-description?redirectedfrom=MSDN

Hope it helps!