Jagex doesn't link accounts together, which means if one account gets banned, they won't just ban any other account connected to the IP, unless they have evidence those are also botted. However they do flag IP's at some cases, which makes your future account more likely to be spotted and therefore banned, if botted. You can always use a Proxy/VPN.
Resetting your modem, regardless of dynamic IP or not, doesn't give you a brand new IP. but rather a new IP in the same range as the previous.