How to estimate average variation of input solar radiation that would be tolerable for a given solar panel? On what parameters will it depend?
There is no limit in how much light a solar panel can absorbs besides of heat limitation for the common crystalline silicon panels.
That being said, it will depend a lot of your solar panel technology, encapsulation and ambiant temperature.
There are several types of solar panels, the most common are thin films, crystalline silicon or concentration cells which can take very high irradiation, but needs optics and only works with a fairly direct irradiation.
The efficiency of solar panel reduce significantly with heat.
Edit following the comment:
It will start charging at fairly low irradiation, a few W/m2.
This is due because of the I-V properties of the photovoltaic cells. The current is linear to the irradiation at short circuit, but the voltage is almost directly at the Voc (maximum voltage) when the circuit is open and the panel receives some light.
If your system is directly connected to the battery, the panel voltage will be forced at the battery voltage and will supply current to the battery at its operating point for that voltage.
As soon you will have some light, a few W/m2, some current will flow into the battery as long as the Voc is higher than the battery voltage.