Heat transfer with surroundings: why considered reversible?
The surroundings are typically modelled in thermodynamics as an ideal (reversible) reservoir with infinite heat capacity and negligible temperature gradients (i.e., infinite thermal conductivity).  The assumption is that the temperature gradients are confined to the system, rather than the surroundings, and the entropy generation is confined to the system.  Of course, in real life, this is only an approximation.