a)
nothing wrong with landline phones btw, though they're from the Mesozoic era when the dinosaurs roamed around, but they're still useful. Well he's trying to get the average age, contacting all landlines in the city, will give you the contact numbers of those that do have a landline phone, now, not everyone may have one yet live in the city, and likely most these days have a cellular phone.
Now, random sampling 300 folks, doesn't give us a valid value, but it depends on several factors
who picked up the phone? a youngster? a parent?
what time did the mayor call? the person answering the phone depends greatly on the time of the day, could be the teenager, or the maid, or the babysitter, or even a visiting relative.
b)
will he miscalculate the average age?
highly likely, why? because of the reasons above in a).