Woman in iddat leaving the home due to fear of being alone

Q: A girl is currently sitting iddat in her father and mother in law's house.

Her ex husband is a total lost case. The ex husband's parents have decided to let her (their daughter in law) sit her iddat in their own house because she has no where else to go. The ex husband is not staying in the same house as his ex wife.

Also the girl's family, all of them are not on Deen. They are mostly involved in gangsterism and drugs. She has absolutely no where else to go. The only safe place for her to live and spend her iddat is at the home of her parents in law.

The question is, since the girl is spending her iddat at the home of her parents in law, so when they (the parent in laws) both need to go out together for some of their necessities, can she accompany them? They say that they cannot leave her alone at home, as the area is a bit dangerous and also she is scared to stay alone.

So are they allowed to take her with them when they both need to go out?

Wiping a drop of urine from the toilet seat

Q: There was 1 drop of urine on my toilet seat and I first dried the seat then poured water from the jug carefully over the seat, while pouring the jug of water over the seat, some water leaked off the seat to the sides and down to the floor. Was this water that leaked najis? And also someone stepped on that water and walked across the house. Is the carpet in the house najis?

Giving the wife a parting gift after divorce

Q: I am reading the kitaab (Handbook to a healthy Muslim marriage) after learning the fiqh of nikaah.

I'm on page 236... its explained that when a husband divorces his wife, he should provide parting gifts to his wife e.g. a set of clothing. It is the first time I'm hearing of this hence..

My question is, does this happen in our South African community and is the above also known as Mahr Mithal. My Apa taught us about Mahr Mithal from Behishti Zewar.

Changing one's name

Q: I am a girl from Pakistan. My name is Ashna, and I personally do not like it. It is not a religious name, but that is not the reason why I do not like it. I simply do not like the way it sounds or the way it looks. Can I change my name with my parents' permission? Or will it be considered showoff or something else? Should I change my name or not?