Is it possible to route USB 2.0 using regular traces?
It depends on many factors, like what chip are you connecting to, and how long is the distance from connector to chip, and whether you want it to work reliably, or have to pass the compliance testing.
The resitors depend completely on the chip if it requires resistors or not. Some do, some don't.
The USB interface is a differential signal, so it requires a medium with defined differential impedance, to prevent signal reflections at discontinuities. Therefore it must be routed on PCB as a differential pair with defined impedance. I don't know what do you mean with regular traces, as any regular trace on a ground plane is a microstrip. It's just that the trace widths and distances on the ground plane are calculated so that the resulting impedance is suitable.