Can she stay after applying for I-485 and I-130 beyond 02 Feb 2016 or does she need to apply for advance parole and go back to her home country?

Generally, immediately upon filing a Form I-485 Application for Adjustment of Status, a foreign national becomes an Applicant for Permanent Residency, authorized to remain in the U.S. while that application is pending. If a foreign national entered the U.S. lawfully and with inspection, and then becomes married to a U.S. citizen, the foreign national successfully may go through the Adjustment of Status application process even if he/she may have overstayed an initial visa. Additionally, note that while there may be some advantages to supplying a Form I-693 Medical Examination Report with the application forms, that no longer is necessary and may be supplied later. It would be wise to work with an immigration attorney who, after learning all of the relevant information about you and the foreign national, would be able to advise about eligibilities, options and strategies and would be able to offer legal representation in the application process - a process that often can be significantly more complex than it appears.