Is it permissible for us to sever ties of kinship if our blood-relatives` gatherings/meetings involve acts of sin?
Observing kinship ties is obligatory, and paying your blood-relatives a visit causing their sinful acts to be hindered , then you should do so. However, if their sinful acts continue while you are at their gathering and they didn't respond positively, then observing kinship ties via telephone and the like will suffice in this case. And Allah Knows
My father passed away, and he had life insurance with "Alico" for an amount of 12,500 dinars. He had paid premiums totaling 2,000 dinars. The insurance company paid us the insured amount. Should we take it, or is it considered forbidden (haram) money? And what should we do with it if it is forbidden?
You may take the amount your father paid to the company. The remaining amount is not yours. However, if you must take it, then accept it and donate it to the poor. And Allah Knows Best.
Is it permissible to swear by (Allah "The Living")?
Yes, it is permissible because "The Living" is one of Allah`s Attributes.
Is my son who was breastfed one filling time by my aunt considered a brother to her children?
The baby who was suckled five sporadic times by a woman is considered a son/daughter of hers.