Upon increasing the intensity of a light source,

Intensity of light is defined as the total energy emitted per unit area per unit time.

$I = \dfrac{E}{A \cdot t} = \dfrac{n h \nu}{A \cdot t}$

where $n$ is the number of photons emitted in time $t$ and $\nu$ is the frequency of light.

When the intensity of a given light source is increased, its frequency $\nu$ remains constant. Therefore, the number of photons emitted per unit time $\left(\dfrac{n}{t}\right)$ increases.

The total energy of the emitted photons per unit time is the power $P = \dfrac{n h \nu}{t}$, which also increases as $n$ increases.

The energy of an individual photon is $E = h \nu$, which depends only on the frequency and remains unchanged.

The speed of a photon in a given medium is constant and does not depend on the intensity of the light source.