Fiber that runs into your house can work with any fiber-ready router. So, yes, it's a modem in a sense, but also does the router/wifi job as well.

However, if you have Verizon or Huawei device on the end of your fiber line, your ISP can likely connect to that device, specifically for things like seeing if anyone is home. They don't need to do that, as it's only data for them to collect to work out advertising profiles.

Once your data leaves your house and goes into their network, then it's just your data on their network. Yes, they can see the data being routed, unless you use a VPN. So your options are going from your ISP able to see when you're home, to not giving them access to anything and just paying the bill every month.