1. It's fairly easy. If you have trouble, start by saying «др» (or simply try saying "Dracula" with a rolled R), which many people find easier than saying «р» alone. Then try to separate it from the «д» (or "D") sound.
  2. My guess is that it's just for emphasis. In the past I've been criticised by Russians both for pronouncing the sound with too much emphasis, and for pronouncing it with too little. However, I don't think it's all that important - people will still understand you if you over- or under-emphasise it.
  3. I have heard the story about Lenin before from various sources (apparently Trotsky criticised him for it). As for children learning the sound, I think children of any nationality have to learn the sounds of their own language, and sometimes they have problems. My mum is a "speech and language therapist", and she mainly deals with native English children who have problems pronouncing certain sounds (e.g. "really" -> "weally", "yellow" -> "lellow", "sound" -> "thound"). So I wouldn't be surprised at all if Russian children sometimes have trouble with native sounds in Russian.