For privacy, any ISP can technically see everything you do online including phone using wi-fi unless a device or syatem uses a VPN, Tor, or i2p, but that does not mean the ISP is keeping records of what an account does online. They may have no interest.
For security, you definitely need your own router. If you can build a system to use as a router running OpenBSD or pfSense, at leaat use a router with open source firmware so your router traffic is not going to someone else and an open source router will give you a lot more extensive network functionalities.