I'm both hands for keeping the Russian site (rus) for Russian speakers, with Russian as a working language, and the English site (russian) for English speakers, regardless of their Russian level, with English as a working language.
My greatest challenge with learning new languages is inability to comprehend the native forum threads about some language subtlety, because I, first, don't always command over the language well enough to understand the answer itself, and, second, people answering in their own language tend to not keep in mind that the foreigners might be reading them, take understanding of the language for granted and fail to explain things that might seem obvious to them.
This is perfectly normal for a language forum in the language itself, but this might scare the potential learners away.
If we stick to English as a working language (one in which questions are asked and the answers are given) this could become a great resource for non-native speakers interested in Russian.
We don't place any additional restrictions on the questions and answers on top of those already in the FAQ, except that we require that both questions and answers are in English.
If there is a question in Russian, we just move it to rus.se
As for the name of the site, I think something like "Russian for non-native speakers" would do alright.