The reason for the interference pattern is that photon's location in not well defined, the presence of photon in particular place can be determined by probability and this probability is presented as a wave.
Probability distributions have the same meaning classically and quantum mechanically.There is a distribution for life expectancy for example, giving the probability of dying if one is a certain age. This can be plotted in a histogram . The only information it gives is that one event, a person at 90, has a probability of dying within the year of 0.17. The curve was measured from a large sample of population.
In a similar way, the probability curve of a photon impinging on the two slits that it will hit at a certain (x,y) on the screen can be measured by a large sample of photons and one will have the two dimensional histogram of that probability, and then can give a probability for the next photon. Fortunately though mathematical solutions help us to get the probability curve, and those solutions contain sines and cosines which are solutions of wave equations in general, like energy waves and sound waves which have been studied for centuries. The mathematics of quantum mechanics has similar differential equations, but the solutions are identified differently.
that probability wave is splitted in to two while passing the two slits, collide with each other and causes interference pattern.
Question 1: Is this reason for single photon interference correct?
The above preamble is to stress that there is no splitting , there is just a computed/observed probability pattern. There is nothing to collide. It is just a representation that has sine and cosine solutions and a single event will appear according to the probability so that it adds up to the interference pattern. Similar that a single death seems random unless a large number of deaths are plotted and probabilities can be gauged. So no, it is not correct. No splits and interference
Question 2: How is the probability wave behaving while two-photons passing double-slit at a time? Are 4 probability waves (2 for each) interfering?
No, even if you manage to pass two photons at a time (photons are very fast point particles) they do not interact with each other. Quantum mechanical calculations that fit experiments much more sophisticated than the two slits show that photons interfere with each other with tiny probabilities, calculated by higher order feynman diagrams.
BUT two photons can give an interference pattern if superimposed, superposition means adding of wavefunctions so that the measured values show the interference of the wavefunctions. This video is instructive for monochromatic interference patterns.