Is our Belkin router getting hacked?

I don't know of any microwave towers. There are no high power lines for miles. I'm more concerned of others using the router for illegal purposes, more than them hacking into our stuff. But I suppose both are feasible if someone has the know-how.

is because you are sort of isolated, certainly outside the normal footprint area of your neighbors. Someone would have to get near enough to your home to use your wifi. Few routers effectively broadcast usable signal more than a hundred feet or so. Some also have power rating where you can lower the percent of power used for broadcast, to lower the coverage area.

High power lines pick up wireless signals and can carry them along quite a distance in the electic field around them and some of those signals might have been touching your router and still be viable enough to trigger as an attempted connection. That's also why one can take a flourescent tube, plug one end into the ground under them and have it light up. Microwave towers are more obvious.

Unless your router shows these connects as established in the list of users, nothing to worry about.

If you live along a busy road, people with the newer phones that will use any open wifi band may be getting logged into your router.

You really only need to worry if you see someone having a working connection, because they all can "connect" enough to make the attempt to get an IP assigned to them, if they pass the security.

There are so few that do this that want anything more than a hunt for an open system to get banking or other details. Since routers are a natural firewall the defaults nip that in the bud.

And using a router for illegal purposes is well, what would that be? I'm a programmer and more yet if I wanted to do something illegal I would not be pinging routers to find a router I can hack. That's not something that will pay.

--> ROUTER LOCKUPS that cause folk to reboot/power cycle are too common and have little to do with scans and probes from the outside world.