Yep, google it there are toms of examples.

Absolutely. Skin cells, sweat, etc. provides food, they use the fiber for the larvae casing.

No moths do not eat cotton, they can only digest animal material, like silk or wool....but they will eat, as said, skin cells on cotton clothing, so wash your cottons and they will be safe from moths.

It's the larvae of clothes moths that eat. Many of the adults don't have mouths and live a short time. You'll generally see the larvae, or their discarded egg cases, or tube-trails if that's what you have. They don't like cotton, but they will cut through it in search of something better to eat.

Clothes moths can be killed by moth balls (paradichlorobenzene or napthalene both of which can cause a nasty blood disease if you are exposed to too much of it) and red cedar oil. Thus, red cedar balls or lined closets are as effective as moth balls.

Other substances "deter" moths, which means they are supposed to convince a moth flying around in your house to lay eggs elsewhere. Once the eggs are hatched, the larvae are going to eat what they can find, regardless of the nasty smell (lavender is supposed to be nasty to them) all around them.