Is collecting money from participants in a competition to cover the prize's cost considered gambling, and must money be returned to a member who left and refused to take back what she paid for drinks, and must I pay for my friend's conference ticket despite not receiving a refund from the ticket distributor?

Paying a subscription fee to enter a competition is considered gambling, and one must repent from it by returning the money to the participants. As for what the member paid as a gift, it is not obligatory to return it, and she is not permitted to demand it back. Regarding the price of the ticket you were entrusted to purchase, you are not obligated to guarantee its price to your friend unless there was negligence on your part, for an agent is trustworthy and does not guarantee unless there is transgression or dereliction of duty.