Cosmetics are substances or products used to enhance or alter the appearance of the face or fragrance and texture of the body. Many cosmetics are designed for use of applying to the face and body. They are generally mixtures of chemical compounds; some being derived from natural sources (such as coconut oil), and many synthetic or artificial.
No. It is not permissible to display or sell a picture of a female exposing her hair and with make up on her face.
Such picture will promote wrong attitude against women which is used by the sinners who look at the female a source of sexual amusement. Woman is much higher and more noble than to be used as a piece of artwork.
It is very important to have good relationship with your relatives but that should never make you disobey Allah in sitting with females who improperly dressed or wearing makeup. We must avoid such gatherings until the participants make proper sitting arrangement for men and women with out mixing.
If you definitely know that this female will use your beauty services in sinful way, then you should not help her in doing wrong. If you do not know that and they do wrong later on, you will not be responsible of their sinful acts.
Muslim female must keep herself away from harmful exposure to non Mahram men. Full Hijab is must and she should not allow any misuse to her photo or video especially if she is young or looks attractive.
'It is permissible for Muslim woman to teach or guide others through Internet including YouTube etc after being sure that she is abiding to the Islamic teachings which aims to protect her from any type of exploitation.
It is not allowed for any Muslim female to wear any type or any degree of makeup in front of non Mahram men . If your employers force you to put red lipstick or any type of make up in front of men, then you must avoid that even if you have to leave the job if they insist on forcing you to do that, because it is against the teachings of Quran (Tell the believing women to lower their gaze and protect themselves (from sinful sexual acts) and not to show off their adornment except what is apparent .(Sura 24, Verse 31).
Wearing make-up in front of non-mahrams is not permissible according to many scholars.
May Allah grant you success
No Marja' of Taqleed has the authority to go against the Quran. Quran is very clear that showing the beauty or ornamentation is not allowed (ولا يبدين زينتهن) Al-Noor : 31.