Is there sin upon one who opens a page for sports and weight loss with the intention of helping people, while knowing of the possibility that some might use it for bad purposes, or upon one who publishes useful information from a page that contains forbidden images, if the visitor happens to see them?

We congratulate the questioner on his diligent pursuit of the legal ruling, for a Muslim should be an aid to his brothers in righteousness and piety, not in sin, as Allah the Almighty says: {And cooperate in righteousness and piety, but do not cooperate in sin and aggression.} The ruling on social media platforms and modern technologies depends on their usage. They can be a means to spread good and invite to it, which is an act of righteousness and obedience. They can also be used for permissible, disliked, or forbidden matters. These are means that take the rulings of their objectives, so whatever is a means to something forbidden is itself forbidden. You must prevent the dissemination of forbidden content on your page, otherwise, you would be complicit in the sin. As for the information you obtain, be careful not to transmit forbidden images. There is no sin upon you if others view forbidden content on the page from which you transmitted.