Question

does speed of photons in vacuum change with change in frequency

Answer 1

No. The speed of all frequencies of light is the same in a vacuum. What does change is the energy of the photon. (high frequency photons - blue ones - have more energy)

Answer 2

Einstein assumed not, and there are very good reasons for thinking that's sound at ordinary energies. However, there are some puzzles at extremely high energies (e.g. cosmic rays about the GZK limit) that have occasionally led people to wonder whether there is, at very high energies, some frequency dependence to c.