Count degrees of freedom of gauge tensors

Question

For degrees of freedom (dof)

- it is said that spin-1 massless boson like photon has 2 dof in 4d, like U(1) gauge theory.

- it is said that spin-2 massless boson like photon has 2 dof in 4d, like Einstein gravity theory.

>Can we demonstrate the following dof counting of gauge bosons of the 
gauge theories:

>- What is the dof of 3d U(1)$_k$ Chern-Simons theory?

>- What is the dof of 4d SU(n) non-abelian gauge theory?

>- What is the dof of any d-dim Einstein gravity of spin-2 bosons?

Partial answers are welcome

Comments

Just count how many independent polarization vectors you must specify in the initial state (or measure in the final state).