Why do we assume that a photon has encountered only a single collision with an electron in Compton scattering For explaining the experimental results of Compton scattering theoretically we consider a collision between a photon and a free electron and then calculate the new wavelength of photon after collision which is dependent on the angle of deviation. Why do we assume here that the photon reaching the detector has encountered only one collision with an electron, it could have reached the detector after multiple collisions with different electrons which would give different $\Delta\lambda$ for same angle. Is it because a photon colliding with multiple electrons no its path is very unlikely? Also what is the reason for non zero intensity at $\lambda$ other than the two peak ones?
 A: This is basically called the "thin target approximation". The experimental detection rate depends on the product of the photon flux, the target areal density, and the cross section. The achieve a suitable rate, it's better to have more photon flux than more target atoms. Indeed, if the target is too thick, there will be multiple scattering events, and the analysis will be more difficult.
A: Quoting one sentence from the wikipedia page,

The interaction between an electron and a photon results in the
electron being given part of the energy (making it recoil), and a
photon of the remaining energy being emitted in a different direction
from the original, so that the overall momentum of the system is also
conserved. If the scattered photon still has enough energy, the
process may be repeated.

I suspect your confusion here is that the wavelengths received after multiple collisions are well outside the range of wavelengths received after a single scattering event.  Keep in mind that, because Compton scattering is defined as acting on bound (or loosely bound) electrons, the event is inelastic. Some of the source photon's energy goes to breaking the electron bond; the remainder can be derived from momentum conservation rules.
