Is it permissible to speak with a girl you love and who loves you in front of colleagues at the institute or over the phone?

Stay away from this girl and do not speak with her, as there is nothing in Islam known as "love," "acquaintance," or "friendship" between genders. If you wish to marry her, propose to her directly, for marriage is the solution for those who love each other. If marriage is not possible, then distance yourself from her completely. Both of you must fear Allah and beware of what incurs His wrath.