Is it common that small local airports don't have radars?

It is very common for small airports not to have a control tower, radar, or communications equipment. There are very well developed procedures for "uncontrolled airports". There is a standard traffic pattern that aircraft fly at almost all airports (consisting of a downwind, base, final, and upwind leg) and there are specific radio calls that are supposed to be made at certain points in the pattern. Most airports have a fixed base operator to supply fuel and services. They often monitor the common traffic frequency and supply some info to pilots about wind direction and runway in use. There's also a specific way to enter the pattern - usually at a 45 degree of the downwind leg, Yes it's possible for aircraft to collide and it happens several times a year - usually when a low wing airplane is above a high wing airplane in the pattern. Neither can see the other so occasionally that can happen.