How can I tell if someone is accessing my router?

The router logs will tell you. Why is it unsecured? At least turn MAC address limiting on.

It is a given, you have an unsecured router.

Turn on MAC filtering like @DarkScribe said. That’s how I roll. Much safer and easier than that other security crap.

What make and model is the router?

With that info, we can tell you how to access the administration panel and even what links to click that will bring up a list of currently attached devices.