When light is emitted (or received) one photon at a time, what is the duration of each pulse? Is it related to the wavelength? Is it possible to create a laser pulse (or a radio wave) shorter than the wavelength (period of oscillations)?
This depends on the light source, obviously - some sources produce longer pulses and other sources produce shorter pulses. However, the general rule is that the pulse duration is limited not by the wavelength but by the bandwidth of the pulse, that is, the lenfth $\Delta \omega$ of the interval of frequencies that contribute significantly to the pulse's spectrum. Generally speaking, the pulse duration $\Delta \tau$ is constrained by the bandwidth via $$ \Delta \tau \ \Delta \omega \gtrsim1, $$ which is essentially the Heisenberg uncertainty principle minus all the quantum mechanics.
In general, if you want to make a pulse with a single wavelength, then this requires you to have an infinitely long pulse. If you want to have a pulse that's shorter than the carrier wavelength $\omega_0$, then the bandwidth $\Delta \omega$ will be larger than $\omega_0$ and you will have a broad, multi-octave spectrum where your original $\omega_0$ might still be relevant to describe the finer details of the spectrum but will be essentially impossible to infer from a qualitative look at the latter.
For more details, see my answer to the closely related question How can a wavelength be defined for a laser where a photon's travel distance over a pulse duration is less than a wavelength?.