Safety in Cape Town: Myths and Reality

I have a problem. I am really tired of the unstable opinion about safety in Cape Town. Please help me sort out this dilemma once and for all. 1. Is it safe to travel around the city by public transport? 2. Is it safe to travel from the airport to the city by bus? 3. Is it safe to climb Table Mountain alone? 4. Is Cape Town generally safe for a solo foreign traveller? 5. In which areas of the city is it safe to walk in the evening?