Advising a neighbour who abuses a cat

Q: My neighbor brought a cat from somewhere. But they did not feed the cat properly. So my mother gives food to the cat. The children of the family abuses the cat to the point that the cat may die any time if it stays in that house. So can I take the cat from them and give it to someone else without their permission? They throw the cat here and there and hold it by its neck. The cat will not survive if kept with them.

Father assisting one son financially

Q: Should a parent be equal to all of their children in terms of finance and gifts? 

For example: There are 4 brothers. No. 1 is a doctor, set up by the father but paid back. No. 2 is in the business with his father as a partner, also paid back. No. 3 is still studying. No. 4 is an aalim and recently started working in the business. The father wants to set no. 4 up eventually. 

Question: Will it be fair if the father sets up no. 4 in the business, without paying back. Basically giving him a business and not giving any other brother the same.

Women going to the masjid to attend masjid programs

Q: I am a member of a Musjid committee. My question is about the ladies facility at the Musjid. 

Some committee members feel that we must invite the sisters to attend some Musjid programs, especially which take place on special occasions and in Ramadhaan, in the separate ladies facility at the Musjid. There is no intermingling in the Musjid. These programs may also include meals served to them. 

Other committee members are of the view that this must be avoided. 

Please advise which is the correct policy to adopt in this issue.

Asking Allah Ta'ala to take one's salaam and a message to Nabi (sallallahu alaihi wasallam) or a deceased relative

Q: 

1. If a person says, “Oh Allah, please take my salaam and message and esale thawaab to Nabi (sallallahu 'alaihi wasallam) and present it on a gold platter to him" and they proceed to say Bismillah and say Assalamualikum Ya Rasoolulah and say something like today I read this Hadith and explain and give the Hadith like a person is talking to him and then they read 3 times surah Ikhlaas and say Aameen. Is this permissible? If not, does it have any elements of shirk in it? 

2. If a person has lost a loved one and they say to Allah, can you please take my message and esale thawaab to so and so and they proceed to say Bismillah and then they give a message like they talking to the person as if the person was there and then they read 3 times surah Ikhlaas and say Aameen. Is this permissible? If not, does a person get sin for this?

Woman living alone after iddat

Q: Is it permissible for a female after her iddah to remain in the town she was married in? 

She has a teaching post as well as housing. Housing will be in a shared property with a Muslim family if safety is of concern. 

She does have parents but due to the abusive environment she would feel more safe remaining where she is currently sitting in her iddah. Her father is encouraging her to return to live with her parents. 

To my knowledge, a female is allowed to marry/re marry without the consent of her wakeel. Does this enable her to make all other decisions within the boundaries of Shariah by herself or does she now, after iddah, require the permission of her father?