For the first part, think of मेरी माँ being replaced with आप. Then the हैं is just agreeing with the आप. I know it's a bit weird, especially because in other languages, like French and Spanish, you tend to use 'tu' or be informal with your family. However, as emrys29 points out, people can use आप or be formal with whomever they want in Hindi. The general rule is that if someone is older than you, you should use आप, but sometimes even my parents use आप with me.