Normally, in capacitive dropper circuits, I would expect a resistor parallel to C1. I am missing that one here. How would C1 discharge in that situation?
What is the purpose of R1? Usually I would only expect something parallel to C1, but I do not understand the purpose of R1 here.
Both of these have the same answer--C1 can discharge through R1 and R2, like so:
simulate this circuit – Schematic created using CircuitLab
What is the purpose of L1? All I can think of is to prevent voltage spikes.
My best guess is that L1 is there to limit inrush current, and possibly also to improve power factor (though a capacitive dropper is going to have a bad power factor regardless). It will also act as a rough line filter, but this circuit doesn't really need a line filter.
What is the purpose of R2 and is this necessary? The LEDs in series already determine the total voltage that falls over the load.
R2 provides a discharge path for C1 and C2.
I know of light bulb brands that use the exact same capacitive dropper circuit (even with same values for the elements) for bulbs with more or less LEDs. Isn't that actually bad in the sense that more current will flow through each LED when there are less LEDs?
A capacitive dropper is closer to a current source than a voltage source, especially when most of the voltage is dropped across the capacitor. Slightly more current will flow through the LEDs, but not significantly more.
Is there a reason why this is done? Is it just cheaper to produce or is it also on purpose so that it will fail sooner?
My guess would be that it's probably mostly done just for simplicity's sake, so the probably-overworked engineer can get things finished and to manufacturing quickly and move on to the next thing rather than spending time recalculating values for every variant. It's also marginally cheaper, as they don't have to source more different component values. If they wanted to make the LEDs fail sooner, there are more effective ways to do that, like skimping on the heatsink (which they probably did as well).