I normally use Avon products as it is a jewish company and doesn't use alcohol or pig. For a few years i used syrian make up but now that i am ut of syria i will have to get stuff made elsewhere, so avon is wht i will most likely go for.
I am unsure abour carmine. I read that insects werent haram but don't remember where i read that. if that's true, then carmine would not be haram. it's best you ask on islam QA as a scholar will let you know whether insects are haram or not.
Animal hairs and hides from halal animals are halal but what about haram animals such as fox? I m unsure if their fur is allowed.
There are a couple of hadith about animal hide that i remember. One states that every hide/skin that has been treated (in the sun, etc) is clean. كل اباغ ضبغ فقد طهر
Another states that we shouldn't take the hide of a dead animal. الا تنفعوا من الميت بإباغ
I think what these hadith mean that if animal is slaughtered, it's hide can be taken and treated which makes it pure to use. But if an animal has died by itself then it's hide shouldn't be taken for use. Since animals should only be killed for food or self defence, that would mean that in most cases we won't be able to use the skins/hide of wild animals or haram animals. And Allah knows best.
Note: i am unsure of the wording of the second hadith as I memorized it a few years ago.