Emma seems to know when children are lieying; Henry, Ava & Nicholas but her ability with adults is fading. She knew Ragina didn’t really love Henry in the pilot which is why she stayed in StoryBrooke, Mary Margret is not discreet enough, David is a mess and one that I would want to question more than once just because his answer is almost always “I don’t know.”
As for Emma and Sidney I think back to the bar scene where Sidney says “We wont be fooled again.” (or next time.)
Sjm, if there was anyone who could see how the modern world worked outside of StoryBrooke knowing how to tamper with phones I would say 2 people; Ragina and Rumplestiltskin. Especially if Rumple still had the ability to see the past present and future.