A mahram is an unmarriageable kin with whom marriage or sexual intercourse would be considered haram, illegal in Islam, or people from whom hijab is not obligatory.
Your husband's step father is non Mahram to you and to your future daughters as well, simply because he is not the biological father of your husband.
Both looking at non Mahram woman with make-up and mingling with her, are not allowed for Muslim man.
Muslim man should lower his gaze and avoid looking at non Mahram women especially when such looking moves his desire in any way.
It is not permissible because it is a type of touching with cloth with a non Mahram.
Daughter of your half brother is a real niece for you and she is a Mahram for you like your daughter. Your half brother's mother is your father's wife, who is also a Mahram for you like your real mother.
Step-dad of your husband in non Mahram to you and to your daughters. If he has a real son who can enter with you in a verbal temporary marriage contract for a short while with out consummating it , that will make his father (the step-dad) Mahram to you and your daughters. If that verbal contract is done with your daughter, his real father ( the step-father) will be Mahram to your daughter.
This is a very important question, and relevant to all of us, as we all somehow socially interact with others. In today's society, the boundaries of non-mahram interaction are also weaker than before, which makes it even more challenging for us Muslims.
Please watch this presentation I gave in the holy month on this very topic, with detail explanation. It starts from the 1:38 hour mark:
If your adult daughters find it difficult to wear full Hijab at home in front of the Non Mahram man, you must protect them from falling in sin of being seem by him with out full Hijab. You must arrange for him another place to live, away from your adult daughters.
Mahram persons are those persons with whom marriage is always Haraam ( Not allowed for life) e.g. for male: His mother, his real sisters, his daughters, his wife's daughters from previous marriages, his real aunts, his father's wife, his daughter in law ( wife of his real son), his daughters' daughters, his sons' daughters.
Mahrams for female are e.g. Her father, her real uncles (Real brothers and real sisters of father or mother), her sons and their sons, her daughters' sons, her daughters' husbands, etc.
If the marriage between your father and her was consummated, she became your step mother and a Mahram for life even if she is divorced later on from your father.
If she has fulfilled her duty in Hijab, she will not then responsible but the man who looks at her with lust will be responsible of his evil thoughts. Men must avoid looking with lust to females especially who have done their full Hijab.
Muslim man is not allowed to meet and chat with women who are not Mahram for him unless in emergency or medical or security necessity. No friendship is permissible between male and female out of the discipline of marriage either permanent or temporary. If they go to public places with their families and they meet there by incident and with out planning, they should avoid chatting and mixing with non Mahram.
If they are mahram to each other then holding hands is permitted. So if they are 'engaged' meaning that they have either conducted a temporary or permanent aqd which has been read for them, then it's ok. If neither have been read for them yet, then they aren't allowed to physically touch each other regardless of what the parents say.
May Allah grant you success