Easiest, most practical, 90% good enough: Get your IP address, grab your phone on mobile network and go to http://your.ip.address

So, if I was exposed I will see the router's login page?

If you're running their equipment, you may see your ISP provided modem's login page, which ideally should have whatever randomly generated password was on the sticker on the bottom of the modem when you got your service. A shade more secure than a router with default credentials.

I'd hope you don't even see that. Your ISP shouldn't be exposing that to the internet by default, either. Ideally you get connection refused or an eventual timeout.

Run a port scan on your public IP address.

Plenty of websites allow you to do it, although it's probably safer to grab a shell on any other host connected to the internet (could be even just your phone connected to its mobile network) and run a port scan (e.g. nmap) from there.