All perfect praise be to Allaah, The Lord of the Worlds. I testify that there is none worthy of worship except Allaah, and that Muhammad is His slave and Messenger.
It is permissible to teach this subject provided that you clarify to the students the religious prohibitions that may be found in some transactions. Also, you should clarify to them the good characteristics of the Islamic legislation and the disadvantages of Riba (interest and usury) and its bad effects on the individual and the society. The best evidence about this is the current world financial crisis. By doing so, you would have benefited from that in calling people to Allaah and it might be that Allaah will guide some people thanks to you. For more benefit, please refer to Fatwa 86231.
In addition to this, it is permissible to teach the Muslim students even if there are some disobedient ones amongst them, but you should exploit the occasion to call to Allaah, as we already mentioned.
As regards teaching in a place where the male and female students are mixed, then if there is a separation between men and women while the women are dressed in Hijab, then this is permissible, but if the situation is like the case in many educational institutions, where there is a disgraceful mixing of sexes and where women do not wear Hijab, then this is a great means of temptation. In which case, it is not permissible for a Muslim to work in such a situation unless there is a preponderant benefit and the Muslim is safe from the reasons of temptation. For more benefit, please refer to Fataawa 84281 and 82730.
As regards some suggestions which you asked for, then we advise you to seek the help of some pious Muslims who are experienced in this field as they are the ones who are best positioned to help you in this regard.
Allaah Knows best.