Talaaq

Telling wife that we are separated for 40 days

Q: I got married last year and it was a love marriage. I moved abroad and my wife is still back in my homeland. We fight alot. Before and even after marriage, we beat each other, obviously I am the husband so I beat her harder.

Now, every time we fight, it ends with her asking for talaq, or I tell her to leave me, or I tell her everything ends etc. But recently in messages, we fought again, and as usual she asked me for talaq and this time I said to her that we are separated for 40 days. Then I blocked her from every social media that we keep contact on. I haven't called her or said any words of talaq. 

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. 

Words that do not constitute talaaq

Q: I have a few questions regarding whether talaq takes place in these circumstances.

1. If a person says 'Recharge' or 'Macho' aloud with the intention of divorce, does this count.

2. I was uttering 'Salamu-alaykum' repeatedly with no intention. On the last time, when I reached 'alaykum' the thought and intention to divorce came to me. Does this take place?