Electric field in a resistor
Yes.

There's even a well-known form of Ohm's law,

$$\vec{J} = \sigma\vec{E},$$

that expresses the effect this field at each location in the resistor. Here,  \$\sigma\$ is the material conductivity, \$\vec{E}\$ is the electric field, and \$\vec{J}\$ is the resulting current density.

You also know that potential difference is defined in terms of the integral of electric field:

$$V_{ba} = -\int_a^b \vec{E}\cdot{\rm d}\vec{\ell},$$

where \${\rm d}\vec{\ell}\$ is an infinitesimal element of the path from location a to location b. This tells you there can't be a potential difference between two positions (like the two ends of a resistor) if there is no electric field on the path between them.