Are photon absorption and emission instantaneous? Is photon emission from an electron transition instantaneous? I don't mean the lifetime but I am asking about once that time ends does electron transition instantaneously? Similarly for the radiation reaction force once the photon is emitted does the momentum of emitting particle change instantaneously, or does the force act for a certain time? If it takes some time, doesn't that violate the conservation of energy, since the photon has been already emitted and the electron is still continuously changing its momentum and energy? Similarly in Feynman diagrams, when a virtual photon is emitted or absorbed does momentum change continuously or just instantaneously for both the emitting and absorbing particle?
 A: Your question confuses concepts of classical mechanics and electrodynamics, with the behavior of quantum states that necessarily differ ( that is why quantum theory had to develop).
You ask:

Is photon emission from an electron transition instantaneous? I don't mean the lifetime but I am asking about once that time ends does electron transition instantaneously?

In quantum physics there is no way to predict the behavior in space time of a single particle, photon in your question. Only the accumulation of many events with the same boundary conditions can be predicted.  In the case of electron transitions in atoms this means the lifetime can be predicted, an accumulation of similar events. There is no end of lifetime as you think.

Similarly for the radiation reaction force once the photon is emitted does the momentum of emitting particle change instantaneously, or does the force act for a certain time?

The same as above, there is no sense for individual interactions, only probability distributions can be predicted at the quantum level.

If it takes some time, doesn't that violate the conservation of energy, since the photon has been already emitted and the electron is still continuously changing its momentum and energy?

As it does not have a meaning to say "takes some time" there can be no violation.

Similarly in Feynman diagrams, when a virtual photon is emitted or absorbed does momentum change continuously or just instantaneously for both the emitting and absorbing particle?

The probability distribution is the only predictable numbers in quantum physics observations. The Feynman diagrams are a tool to calculate those distributions.
Maybe if you read this answer of mine you will see how probability distributions build up in quantum experiments.
