I used to log in on one account thru the rs client then i would open my bot client on unsigned. I've also heard that you could click both browsers at close to the same time and it;ll work.
I just did today. Just take two browsers and enter username and pass on bolth then take one browser and let it keep its height but make it like half an inch wide and scroll so u can see the login button and then meve it right next to the other login button then as fast as u can click the small windows button then the big windows login button and they should bolth be logged in.
I dont know if a proxy you can log in rs with, but proxies are used to get passed block websites, such as facebook, youtube, at school, etc.
It is a different ip than yours, so you should be able to multilog into the same world fine.
Only one i know is hidemyass.com, but you could check google for more.
Yes, with out using a bot client you can do but the accounts have to be on different worlds, if you want them to be on the same world then you have to use swift kit or rsbot.