Is it permissible to work for a company that designs and sells websites, without knowing the uses of the designs or the nature of the websites in which they will be used? And does the designer bear a sin if his design is used in a deviant and corrupt website after it has been sold?

It is permissible to design websites, unless the designer predominantly believes that the client will use it in disobedience to Allah Almighty. If it is used in disobedience, then the sin is on the user, not the designer, for Allah Almighty says: "And no bearer of burdens will bear the burden of another."