Two excellent questions. Here are the answers.
First, we ran a study to see whether children could detect children's lies better than chance. The answer is no. Interestingly, those who lied themselves were biased to think other children were liars. Nevertheless, this bias did not help them detect other children's lies any better.
Second, children begin to tell lies at 2 but suspect others to be lying to them after 5. The reason is that we as humans are perhaps biologically programmed to trust others to tell the truth. Also, statistically, others tell the truth to us far more frequently than they tell lies. So, it is a highly adaptive strategy to be more trusting of others. The downside is that we are not very good at detecting others' lies.