Anyway, strange things have been happening like passwords not working on some websites like as if they been changed, sometimes I log into my mail box and find mail I read last time now appearing as unread and a few other oddities.
Web traffic is pretty much completely SSL and HTTPS, particularly logins. Even if we start with the assumption that the router was under malicious control, the web traffic where you log in and view your E-mail could not be inspected to get your password, nor could those communications be changed since they are encrypted entirely to prevent tampering between the client system and the server.
The "System Log" information indicates nothing untoward. The IP address is probably because a system connected to the router requested it- it's an ad server so it's going to be pretty common.
"Run Manual set APN" likely means a client is connecting- APN is "Access Point Name".
Fact is if they were spying,
you wouldn't know . Somebody "spying" on your web activity even with full direct access to your PC doesn't want to be detected and isn't going to leave log entries or start changing your passwords one at a time, or log in to your webmail and arbitrarily flag read E-mails as unread again.