First of all, I personally really don't think Chinese and Russian share similarities in pronunciation. Russian to us, at least to me, sounds like French, people have to have a rather flexible tongue to speak such languages, I think. It is too beautiful for me to learn.
Second, I think there actually is R in Chinese. It's just we don't have 'Ra' as in Russian, but with other vowels as in 'ri', which means 'the sun', or 'ri ben'-Japan, 'ren'-people, 're'-hot, etc.
'Russian' spelled by Chinese pinyin would be 'ra shen'.
There is another thing, although Chinese does have R, it is a little difficult for people from certain regions with a strong accent to say, as Chinese Mandarin is basically based on northern pronunciation, since the capital Beijing is in the north.
By the way, I love Russia and really hope I could see the Red Square one day in person, other than from telly. LOL.