What is the quickest way to bring my foreign fiancée to US? Can we visit each other as either application is in process ?

Significantly more information is needed in order to provide a legal analysis of ways your fiance may be able to attain immigration benefits. This includes, for example, information about your own immigration status (Are you a U.S. citizen? Are you a Permanent Resident? Do you have some other status?); information about your fiance (What is her nationality and immigration-related history?); Etc. There really is no substitute for you and your fiance to consult with an immigration attorney who, after learning all of the relevant information, could advise about eligibilities, options and strategies to attain your goals, and who then could offer legal representation in the often complex application process.