My father lived and died in state of New Jersey. We are living in foreign country with my mother, and brother, and I have to arrive, and take care of the issues connected with inheritance. Can I act as the next of kin, or my mother should give me a power of attorney - so I could do on behalf of her?

Did your father leave a will?

No, he didn't

What has to be "taken care of" is there a will, is there bank accounts, is husband and father still married ?

If bank account, whose names are on the bank accounts besides fathers.

But yes, you may need a power of attorney from mother or be appointed over the estate by the court

He was found in his flat - and it's sealed by police now. He had a bank account on his name, without "POD" - I don't know what is a current balance of the account. He had a car as well. Parents were married.

Was he still married to your mother? If so, she should be the main heir. In which case she can give you POA to act for her.