Can two collinear beams of two different wavelengths generate the sum frequency or they need to pass each other at a certain angle. For a monochromatic light how does the sum harmonic gets generated while for two different beams a certain angle is necessary?
for any frequency generation process, we need two conditions: frequency match: $$\omega_1+\omega_2=\omega_3$$
phase matching: $$k_1+k_2=k_3$$
for more information see this: Saleh_Fundamentals of Photonics_2007, chapter 21
As long as we deal with linear medium and linear sensors, mixing two sine waves with different frequencies would not produce new frequencies (sums, harmonics, etc.), regardless of the angle between the beams, i.e., the spectrum of the combined wave would consist of two spectrum lines, corresponding to the two original waves .