What is the ruling on working and investing in internet cafes that some people frequent to access prohibited websites? And is the owner of the cafe held accountable for the sin if he merely offers advice, due to his inability to monitor completely?

It is not permissible to work or invest in internet cafes unless they are free of forbidden acts, by preventing visitors from accessing prohibited websites through blocking them or expelling them if they insist. This is based on the Almighty's saying: (And cooperate in righteousness and piety, but do not cooperate in sin and aggression), and His saying: (They did not forbid one another from a Munkar [wrongdoing] that they committed). If it is not possible to control the cafe and prevent forbidden acts, then it is not permissible to open it to avoid sin. And whoever gives up something for the sake of Allah, Allah will compensate him with something better.