Can we use photons in a Bose-Einstein condensate? If not then why? If yes then how? Can we use photons in a Bose-Einstein condensate? If not then why? If yes then how? Which kind of boson are we using in Bose-Einstein condensation?
 A: 
Which kind of boson are we using in Bose-Einstein condensation?

Honestly, any boson that is experimentally feasible to trap, cool, and manipulate. To get a BEC, you need to start lowering the temperature, for which you need laser cooling. For laser cooling, you need lasers that address the specific atomic transition, and you look for ones that are commercially available. Up to now, people have Bose condensed H, He, Cs, Li, Na, Yb, Sr, Er, Dy, Ca and Cr, Rb, and K. Multiple isotopes. I heard they are trying Ti and Fe. The other day there was a paper on arxiv about Europium in a magnetic trap. Molecules formed by Fermi-Fermi or Bose-Fermi mixtures of the species listed above. Also, quasi-particles like excitons, polarons, etc.

Can we use photons in a Bose-Einstein condensate?

See this question and the answer.
Short answer: no, you cannot use free photons. Because they have zero chemical potential. You can, however, use photons in a cavity and dye in order to force them to interact among each other.
