Disconnect from the Internet and monitor the firewall. If there are attempts to send emails out while you are typing something, there could be spywares or viruses on your computer.
Then connect to the Internet and do something like reading an email. Set up a fake email account with a simple password like 1234567890, and use AVG to monitor if there are out-going mails. Your firewall could help, but firewall logs are harder to read. If there's nothing fishy here, it could be the games you are playing that are infected, especially if you downloaded them from crack sites.
Port 10110 is used by AVG. You can read more about it
hereFor port 10060, it is a common connection time-out error that usually appears when the client does not receive a response from the server for a specific command.