Is it permissible to take profit when purchasing an item from the internet for work or for relatives without informing them, and how can one dispose of money previously acquired in this manner?

Taking others' money without their knowledge is not permissible, because their wealth is sacrosanct and is only permissible with their consent through a legitimate contract. Therefore, one must agree with them on the nature of the work and its compensation, or buy the commodity with your own money and then sell it to them for an agreed-upon increase. Whatever was taken unlawfully must be returned.

As for profiting from a bank card: If you take the price from the buyer and then pay it for a known service, there is no harm. However, if you lend money to the buyer to pay the price, and then they return it with an increase, this is prohibited usury (riba).