1. Does the photodiode generate photocurrent when it emits light under forward bias? Why can't photodiode work in forward bias state?

You can look at the volt-ampere characteristic curve of photodiode. When it works forward, it works like an ordinary diode, with unilateral conductivity and DC voltage, and the current is exponentially related to the terminal voltage. Only when working in reverse, the reverse current is called dark current, and the current generated by illumination is called photocurrent. When the illumination is constant, the photodiode can be equivalent to a constant current source. When the photocurrent is greater than several tens of microamperes, it has a linear relationship with the illumination. In the third quadrant of the volt-ampere characteristic. For details, you can look at the analog electronic teaching materials.