Google has a tool to do an account security checkup
It will show a list of security checkpoints. Each of them will contain a list of items to be reviewed by you including a link to a help article that explain each risk.
Suspicious access to my Gmail account from "Authorized Application"
Regarding the "Can't reach this page", the most straight forward solution is to clear the cookies and delete the cache of your web browser. Then sign in again to your account.
Regarding being lock out from time to time, for security reasons, Google will ask to sign-in again in the web browser every certain time.
On https://hangouts.google.com or https://gmail.com
Double click the contact to report to open the chat window
Click the gear button
Click the Block & report button
Check the Also report checkbox
Older related Q&A (they don't mentions the above steps)
How do I report spam/scam attempts in Hangouts?
How do I report scammers on Google Hangouts?