Will changing router modem change my IP address? ?

The publicly IP is normally dynamic and changes each time you reboot the router but the LAN IP does not change. However, if you change the router, you will almost certainly get a new external IP, and quite probably a different internal IP.

Buy a VPN like Cyberghost, NordVPN.

That depends a lot on your individual ISP. If your IP address is account-based, such as by DSL login or by assigning the IP to whatever MAC address your currently registered cable modem has, then changing it is completely useless. If it is dynamic, then actually replacing the hardware is probably unnecessary; you can force an IP change just by changing the MAC address of your router, or whatever device is attached to the modem. 

waste of time even explaining it to you , idiots dont understand plain english .

No. I don't think so.

No!  Your IP Address is provided to you by your ISP (Internet Service Provider).  You could try changing your ISP, but your IP Address MAY be 'transferred' from your old ISP to your new one.

It will not............

They ban you and your computer, not a specific IP address.

Also it is a _criminal offense_ to break the rules of a website, with a penalty up to six months in prison per instance.

Facebook, like most other sites, just ban troublemakers rather than prosecuting, at least to start with.

However they do prosecute repeat offenders and several thousand people a year end up in court due to them making formal complaints.

No.  changing the router or modem merely changes the equpment.  Your ISP has assigned an IP to your system and even with a new router or new modem your IP stays the same. 

You might try getting a new email and opening a new account with a new name, though from what I understand, that is no longer possible. But what the heck, worth a shot. 

They don't track you by your IP address.