Yeah that makes sense, processing delay is apart of every game but they don't always choose to show it in their ping calculation. Generally CoD did used to do this for every server but it appears they're reducing that so you may encounter some servers where it appears higher in game or some where the ping is exactly the same.
If the ping in game is over 30 ms higher than the Geo ping then the server is under load and you'll have a better experience with another server.
It won't be a used router - we open it to apply the firmware to it but we always take great care when doing so. However, if that's the case then it is likely customs have opened it.
What happens when you try to update it exactly? After you upgrade that issue should be resolved.
Hard to say as you've not mentioned why you were restarting and higher ping could be any number of things. Try out the firmware, if you're having the same issues make a new topic and I'll be happy to help there.
It was released last week so it depends if you've upgraded or not. This one is .219, if you look at the R3 interface on the top right you'll see the version number, if that is lower than .219 then this is newer.
You can see it on the homepage, alternatively it's listed in the bottom left.
You don't need to do either