1. I am not sure I understand the recommendations to 'sign up my wife and kid' also. If the have different names and are separate people, how can we accrue miles to the same 'basket'?
Definitely sign everyone up with their own account. If they are flying, they need to be earning something! No, it won't go into the same basket, but you can use your miles to get a reward ticket for your kid (or any other way you want to work it)
2. If I make a booking for 3 people (say me, my wife and my cousin). In the end of the booking you normally get to give the frequent flyer number. So, do I get the miles for all three journeys? Where is the line drawn? Are the miles counted for who pays, or each passenger gets their own miles (back to question 1).
Every person who FLIES receives their own miles. It doesn't matter who pays.
3. If I make a booking for a return trip to Peru, which say uses more than one airline (which can be from different FF programmes), do I have to collect the miles separately, or do all go to the air carrier which cover the longest route or what?
If the airlines are all in the same alliance, you should be able to book the ticket using your miles from 1 program.
(this one I'm sure someone could expand on).