Generally public speaking is more formal and more clearly articulating. In public speaking, you're usually trying to persuade a group of people to act or think a certain way, so you want to present...
Weather is always the safest topic . Enquiring after mutual acquaintances is also good. Study courses are good with peers if you are both students. World news is OK if spoken of in a neutral...
On average, it is impossible to say how many conversations a person would have in one day. It most cases, it really depends on the person. Hairdressers probably have more conversations each day...