Entering a competition run by an insurance company

Q:

1. Is it permissible to enter a competition run by an insurance company, without becoming involved in paying for any insurance, to enter is free of charge.

2. If one does win the competition, and the prize isn’t a cash prize, instead it is a gift card from a completely separate business, will it be permissible to use this gift card? What should one do with the items won?

Assurance from a service company of replacement or compensation in the event of damage or destruction to a vehicle

Q: Is it permissible to engage the services of an individual or a security company that extends a commitment to safeguard my vehicle, with assurances of either replacement or compensation equivalent to its value in the event of damage or destruction?

Doubted whether one ate after sehri time ended

Q:

1. I am making up the fasts that I missed in Ramadhaan. Today fajr began at 5:52am but I mistakenly assumed it was 5:56am and I can’t remember if I ingested anything intentionally/unintentionally between that time. Can I assume my fast is valid?

2. On another day whilst making up my fasts I was unwell and had a sore throat and was coughing quite harshly. In my head I thought if I vomit or if something comes out whilst coughing then I will be ok with that. Nothing came out after coughing. Is my fast spoiled because of this thought?

Using perfume with alcohol

Q: I wanted to purchase some oud. The person selling it had informed me that to speed up the process of making this oud they use a very little brandy (type of alcohol) in the oud. He also mentioned that the Ulama said it is permissble to use such oud.

Will it be permissble to use this oud? Will there be a difference in the maslah if the brandy is made from grapes or if the brandy is made from something besides grapes, for example it is made from wheat?

Parents being just in giving gifts to their children

Q: My aunt has 4 children, 2 sons and 2 daughters. In our culture mothers give gifts to their daughters and their families (daughter's husband and children) once during the winter and once during the summer time. Is it possible for my aunt to give gifts only to one of her daughters?

My uncle does not work, so she gets the money from her sons. I'm asking this question because we have read that we have to be just in giving gifts to our children.

She got to know that this rule (being just in gift-giving) is valid only when the mother is getting money from her husband.