The Cosmetic Ingredient Review (CIR) reviewed the safety of methylparaben, propylparaben, and butylparaben in 1984 and concluded they were safe for use in cosmetic products at levels up to 25%. Typically parabens are used at levels ranging from 0.01 to 0.3%. They reopened their safety assessment in 2005 and determined there was no need to change their original conclusion. Also, a 1998 study found that the most potent paraben tested in the study, butylparaben, showed from 10,000- to 100,000-fold less activity than naturally occurring estradiol (a form of estrogen).
In short, mineral oil is not toxic. Also, skin does not breathe! This study shows that while the exterior layer does absorb some oxygen from the atmosphere, the result is negligible. You're not going to suffocate your skin.
Yes, formaldehyde is a carcinogen, but low levels (like in cosmetics) does not pose a health hazard.
It's possible that triclosan may be hazardous but I'm not sure where they're getting their info about heart failure and muscle/skeletal function.
Carmine isn't inherently bad (unless you're vegan), but it does have links to asthma and allergies in a small subset of the population.
I hope this helped! I know how frustrating it is to have a family member on the MLM skincare train. The companies spout all this fear-mongering information but you turn around and their products are filled with irritating (and possibly harmful ingredients, ie citrus juice) but it's ok because it's "all natural".