Do bacteria cells have a nucleus?

No they don't, they are prokaryotes which means they have no nucleus or membranous structure in their cytoplasm.

Yes they do because a nucleus is the control center of all unicellular organisms and multicellular organisms.

In red light light because during photosynthesis, the chlorophylls absorb all of the colors but green (thats why the leaves are green) so if they absorb all of them, but mostly red and blue because the chlorophylls work better at 700nm and 680nm, they reject the green color and thats what we see