When Patsy tries going to google.com, her network goes to "Facebook" with a message "unverified server" on all her devices. Leo says there's a chance her home network has been hacked. She should not log into Facebook. It makes sense that Google gets redirected so she can't figure out a solution to her problem. The chatroom says that it could be her DNS server. They advise going to http://220.127.116.11/, and if Google pops up, then there's a DNS issue. If it doesn't, then it may be the DNS has been changed on the router.
Leo recommends changing the password right away, then turning on two-step authentication in the security settings of his account. It'll be a pain, since he'll have to use his phone or the Authenticator app to enter the code to get into his account, but it will be much more secure.
Dennis got hacked in a similar way to Mat Honan. The hacker stole his Twitter handle and Twitter won't give it back. He could fill out a ticket that someone is impersonating him on Twitter, but the sad fact is he may not ever get a response. It would be great if Twitter had additional levels of security, but they aren't there yet. Twitter isn't making any money and it's a free service, so they're not motivated to really go the extra mile.