Does emission of electron depend on colour instead of brightness of light?

According to photoelectric effect we consider light to be particles to justify the threshold wavelength in light.
It says that the energy of electron emitted depends on wavelength of light that falls on it rather than the intensity of light.

Intensity is the number of photons that fall on surface per unit time. It ultimately translates to energy because:

No of photons incident per unit time =
Total energy of electrons incident per unit time / Energy of one photon

It was found that if we increased the total energy of electrons incident per unit time it did not knock off electrons.

We accepted the photoelectric effect theory because in experiments we did not find electrons emitted even when high power bulbs or bright bulbs were used instead they were emitted when wavelength of light was least basically the light made to fall was more on the start of the spectrum of vibgyor that is violet and indigo have more ability to knock off electrons.

Is it right to conclude that whether the electrons will be emitted or not or the kinetic energy of it will depend on colour of light instead of its brightness?

Saturation current is when increase in anode potential does not affect the magnitude of photocurrent. Why does increasing intensity increase saturation current?