Studying in school, college or university with non-mahrams

Q:

1. Is it permissible for a man to study in a school, college, or university where he is studying alongside a non mahram woman. And is it permissible for a man to teach a non mahram woman and is it permissible for a woman to learn from a non mahram man.

2. Is it permissible for a woman to study in a school, college, or university where she is studying alongside a non mahram man. And is it permissible for a woman to teach a non mahram man and is it permissible for a man to learn from a non mahram woman.

Observing purdah with non-mahrams

Q: A family member who lives seperately sleeps on my bed sometimes (her husband returns home late at night due to working overtime or night shifts and she is afraid to be home alone at night) my brother who is 15 years and I share the same room, we have our seperated beds. She doesn't observe purdah with my brother even though he is a ghair mahram to her. My question is, will I be sinful for allowing her in my room while my brother is there?

Using freelancer.com website

Q: There is a website called freelancer.com , where a person can hire graphics designers, website designers and the like, to do work for him. One option available is called a contest, where one posts ones requirements and the price he will pay, the money is charged by the website, then various graphics designers who want to offer their services (optionally) create mock ups / designs which the person can then choose between. Sometimes over 50 different designs are made. The person then chooses the one he likes the most. The website transfers the money to that designer, together with taking a small percentage fee for using their platform. The one designer who's design was chosen, will be paid. The remainder who's designs weren't chosen, and had voluntarily posted designs in the hope of winning the contest, get paid nothing. Is this type of contest / ijaarah permissible?