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?