A chiral absorber of light can emit spin-polarized (circularly polarized) thermal radiation based on Kirchhoff's law which equates spin-resolved emissivity with spin-resolved absorptivity for reciprocal media at thermal equilibrium. No such law is known for nonreciprocal media. In this work, we discover three spin-resolved Kirchhoff's laws of thermal radiation applicable for both reciprocal and nonreciprocal planar media. In particular, these laws are applicable to multi-layered or composite slabs of generic bianisotropic material classes which include (uniaxial or biaxial) birefringent crystals,(gyrotropic) Weyl semimetals, magnetized semiconductors, plasmas, ferromagnets and ferrites,(magnetoelectric) topological insulators, metamaterials and multiferroic media. We also propose an experiment to verify these laws using a single system of doped indium antimonide (InSb) thin film in an external magnetic field. Furthermore, we reveal a surprising result that the planar slabs of all these material classes can emit partially circularly polarized thermal light without requiring any surface patterning, and identify planar configurations which can experience nontrivial thermal optomechanical forces and torques upon thermal emission into the external environment at lower temperature (nonequilibrium). Our work also provides a new fundamental insight of detailed balance of angular momentum (in addition to energy) of equilibrium thermal radiation, and paves the way for practical functionalities based on thermal radiation using nonreciprocal bianisotropic materials.