Coherent sources can have ultra short pulse durations
You are talking of the classical electromagnetic wave. The classical wave knows nothing about photons.
provided there is at least one photon in frequency that span broad bandwidth (and are coherent)?
One photon has no width in the framework of the current knowledge of physics. The photon is an elementary particle , a point particle , in the standard model of particle physics, i.e., has its values at an (x,y,z,t) point. Its values are energy=hnu, direction of motion, and spin + or - to its direction of motion . That is all. It is described by a quantum mechanical wavefunction, which is a complex function, Psi, whose Psi*Psi product gives the probability density for a photon to appear at an (x,y,z,t).
Does that mean that the pulse duration is infinitely long for beam of single photon (basically one frequency)?
There is no pulse duration for a photon, it is a disturbance in the four dimensional space carrying a specific energy and always traveling with velocity c.
Here is single photon at a time experiment of "photon scattering off double slit "
Note how the single hits accumulate to give a classical electromagnetic wave interference pattern. This pattern is the probability density distribution of the wavefunction of the system "photon scattering on double slits".
Can we define precisely a photon energy or is it also uncertain?
Its energy is defined by the frequency of the beam that will emerge from many such photons. It depends on the delta(energy) of the atomic transition or the compton scatter etc. A bunch of photons can have a spread in frequencies due to the energy width of the atomic or molecular transition that created them, (or the scattering setup) but a specific photon has an energy and it fixes its frequency by nu=E/h.
What happens with photons and the classical light beam where the terms "pulse" and "coherence" are clearly defined needs quantum field theory to be understood/modelled mathematically.
Hand waving :
Both the classical electromagnetic wave and the photon wavefunction depend on Maxwell's equations. The photon wavefunction obeys a form of maxwell's equations, and it is not surprising that the same frequencies appear, except that in the case of the photon, it is connected with its energy. The electric and magnetic fields of the classical em wave are built up by a superposition of the wave functions of innumerable same frequency photons. These complex wave functions have the electric and magnetic potentials in exponents, where also the frequency and the phases reside . When the functions are superposed and the Psi*Psi is taken, i.e. a measurement, an observation, the classical electromagnetic wave appears.
When one has a classical beam more complicated than a plane wave, the mathematical complexity of going from the photon quantum mechanical level to the classical light increases . It is not necessary though, because one has shown that the classical emerges from the quantum level, and one can trust classical Maxwell equation solutions to work perfectly, as long as one does not go to one photon at a time, where the quantum mechanical boundary conditions have to be considered. It is simple for the double slit , because it is still plane waves classically.
So the energy of a single photon depends on its production way, and that is subject to the quantum mechanical uncertainties and thus has a heisenberg uncertainty in the spread of the energy by its production. Onthe detection side, an equivalent quantum mechanical reaction will also obey the HUP.
There is only one photon , an elementry particle , and there is no pulse duration in the classical sense. Again the production and detection mechanism of a single photon will have a duration within the energy/time form of the heisenberg uncertainty, but is is a single photon, not a pulse.