Outlook vs. Gmail inbox Tug-of-War

I’m an Outlook novice.

I’m using Win 10, Outlook and Gmail (one account; set to IMAP; POP disabled; Auto-Expunge enabled; one filter that came with Outlook: “Clear categories on mail”).

Outlook shows two inboxes. One is in Outlook’s default Personal folders. The other is under the name of the Gmail account.

Outlook’s mailbox structure

Question: Which Outlook inbox should get new Gmail messages?

Question: Without using a filter, is there a setting to direct Outlook to use the inbox I choose? If I use a filter, what’s the best way to design it?

Question: Is it normal for sent messages to appear in both Personal Sent and Gmail Sent folders?