The easiest option might be to ask your friend to pay the fine and reimburse her

Welcome to our NS Community, Anastasia Catanese. Your friend will receive a letter with payment instructions. You should be able to pay this bill with an Italian bank account. Otherwise Jan Haverkamp's advice is a good one.

You can call the customerservice and explain you get the fine because you  couldn’t show your ticket on that moment. Maybe you don't have to pay the fine if you can show the ticket now.

Your phone battery is your responsibility. If it died, you didn't take your responsibility and you get a fine. NS said it in an advertisement campaign, so they're in the right to fine you. If there was another reason the phone switched off, and if that reason allows you to turn it on again, you should not be fined, as you could show it later.

It's clearly stated you don't get a refund in case your phone battery is empty.

You can do transfers from any bank account in the EU to any other bank account in the EU. You just need the IBAN of the destination account.