Is it permissible to accept 600 Euros, which is a prize from a competition held by someone who offers lessons on earning profit from the internet, and which he sends to the winner via his bank account?

If the content of the channel does not contain any Sharia-prohibited elements, and participation in the competition is free, then there is no harm in its prizes. Ibn Uthaymeen issued a fatwa permitting this if the prize comes from an external, donating party and not from the participants themselves, as this would not be considered gambling (maysir). The Permanent Committee mentioned that free cultural competitions are permissible, but if participation requires paying money, then it falls under prohibited gambling.