Is it permissible to earn money from the website "PROTYPERS" merely by entering data (CAPTCHA), knowing that registration is free and profit is earned for every 1000 images?

What you mentioned in the first method, regarding the work being time-bound from 5 AM to 6 AM, with the condition that the worker completes a thousand images to be entitled to the wage, is considered a type of ijara (leasing/hiring) about whose permissibility there is disagreement. The majority of scholars hold it impermissible due to jahala (uncertainty) and gharar (definition) (excessive risk/deception). In contrast, Abu Yusuf and Muhammad, the two disciples of Abu Hanifa, and others, deemed it permissible. This is also the view favored by the European Council for Fatwa (definition) and Research, because combining the two conditions should not lead to impermissibility; rather, they serve the interests of both parties. Accordingly, there is no harm in the mentioned method if the ijara is conducted for something permissible according to Sharia (definition).