What is the ruling on teaching programming and web design? Is the earning permissible? Is the teacher sinful if the students use what they learned to design forbidden websites, knowing that teaching how to embed images, in general, is fundamental to design?

Your work at the vocational institute, teaching students website design and graphic design programs, is permissible, and your salary is lawful. If some students use this knowledge for forbidden matters, you bear no sin, and it does not affect the lawfulness of your salary. However, you should advise the students and warn them against forbidden acts.