Hi!

I have a few questions:

What is going on?

See my other reply. Do you have a light switch that glows when you turn it
off? This will place a small amount of current flow across the lamp, which
may make it flicker.

Will it wear out the bulb very fast?

It may result in a slight amount of wear on the bulb, but I doubt the change
in lifetime would ever be noticed.

What is inside these bulbs? A rectifier? A capacitor?

In many cases, these bulbs contain a small switchmode power supply. Such a
power supply will have a transistor, some type of controller, a small
transformer and some support components (of which a capacitor would probably
be included). Others use a much simpler transformer design.

William