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I think it is always recommended to perform cell and atom relaxation before starting Phonon calculation. After relaxation the structure represents temperature of 0 K (local minima of potential energy surface). But how about the scenario if I use a structure whose lattice parameters given are at finite temperature.On that time, I can only perform atom relaxation. I cann't perform cell relaxation because if I do that the lattice parameters will be changed and it will represent 0 k rather than finite temperature. Finally, the question is, at finite temperature would we get negative frequencies at any q points? If we get negative frequencies, is it normal at finite temperature?

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If you perform an atom relaxation before the phonon, you also get a 0 K result wrt. atom positions. You will need to perform an MD simulation to simulate effects from temperature properly.

I would also consider looking at phonopy and phonopy3 as they can do some quasi-harmonic corrections which include the influence of temperature but within some approximation.

The negative frequencies you see are likely due to numerical precision or the minimum being meta-stable. Indeed, some structures are only stable at higher temperatures and will show negative frequencies at 0 K approximations. This is "normal" to see but not correct as there should not be negative frequencies in a real system unless it is undergoing a transition.

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