re: your first point, what helps me is to know that those people are their for the exact same reason you are.

you're their for mcdonalds, they are their for mcdonalds

you're their to do shopping in a supermarket, so are they- they are just going about their business, just like you

and in this situation: you're waiting in a car. the probibility of someone actually getting in and physically harming you is so unlikely. drive around a bit until he's ready to meet you, have your windows closed, do what ever you need to do to make you feel safe

as for spiders, the spiders more probably scared of you, than you of the spider. they are their so they can build webs and catch flies, not bite people.