Custody of children after divorce and purdah with step siblings

Q: I am divorced with two children (boy 9, daughter 7). My ex wife, has as I am led to believe, settled down perhaps made or not made nikah with the man I accused her with whilst we were married. I am not sure but I assume he is also divorced, he too has two kids of his own, also a daughter and a son I think maybe a year older than each of mine.

My first question is: What is the most authentic ruling regarding custody of children post divorce? Where and with whom and from what age should they reside with either mum or dad purely from what Shariah explains?

My second question and this is what haunts me: If tomorrow they all decide to move in together and lets say they are indeed married for purposes of this question, how does the mahram thing work? This man, is he mahram for my daughter firstly. Secondly, his children being exposed to my children, I fear abuse, bullying, sexual abuse(possibly! as a parent this thought lingers as they grow older and left alone), and my children being teased by his kids - that they only in that home because my ex wife married their father. Tomorrow if these step brothers or sisters or whatever they will be termed, if their natural father purchases or does something for my kids , they could get jealous or nasty towards my kids, maaf but all of these scenarios seem to be playing out, hence my questions. 

Selling samples

Q: I am a Muslim and a doctor. In our country, Medical Representatives (all pharmaceutical companies) visit us with some physician samples daily and we receive it. Few of them we provide to some poor people, and most of them we sell it. By selling it we get some money. And we use this money for our personal use. As a Muslim is it halal or haram for us? 

Taking an interest bearing loan to start a business

Q: I live in a country where all systems of the government are un-islamic. Most of the time our non-Muslim counterparts enjoy all the benefits from certain policies of the government. For instance, the government set aside a multi-billion amount of money to help small, medium and large scale entrepreneurs with a single-digit interest loan, having a single-digit interest loan by a good entrepreneur is viable but for the Muslim, even less then 1% interest is haram.

Consider myself as a case study, I have a viable business idea and I spent almost a year finding a way and manner to finance it, by either interest-free loan, partnership or any Islamic accepted way but I couldn't get it. As a professional accountant I have a "masters degree in accounting and financial management". I know how to secure and manage the government loan but I doubt whether or not it is permissible in Islam when considering the above situation.

Nikaah performed in the state of janaabat

Q: If a woman or man bathed before their nikah and didn't know they had to rub their scalp but every strand of hair (atleast they thought) was wet would this mean the nikah would be invalid as ghusl was not done completely? What about a woman who bathed after her periods before her nikah and missed some parts of ghusl but thought she was cleans. Is nikah invalid?

What if she did ghusl like this for 4 or 5 months after nikah and did ghusl like this after periods and sex? Does nikah invalidate? What if any part of the ghusl was done incorrectly or missed what is the effect of nikah? Is it invalidated?

Women going out to work

Q: I am a shy, introverted Muslim woman. I do not like being around many people, I like to keep to myself. I love staying at home, but my family wants me to work. I cannot find a job that suits both my personality and me as a Muslim woman. And I do not have a skill, like sewing, to make use of and work from home. What should I do? Is it wrong to want to stay at home and not be outside?