Is it permissible to establish an electronic website for a mixed club (girls and boys) concerned with humanitarian activities and collecting donations for those in need, knowing that there is respect and boundaries in interactions between members?

The activities mentioned are good deeds, and assisting in good deeds is no less in reward than performing them. Therefore, if creating a website for the club leads to performing good deeds and occupying oneself with them, then you may create this website. As for the mixing of genders in the institute, that is separate from creating the website, and those responsible for the institute should be advised to prevent unlawful mixing.