Why are old halachot retained in the mishna?
In general, the hachamim based their statements on Torah verses (אסמכתא). As explained by R Nahman miBretslev - the halacha is the ikkar that you rely on and examine carefully, the pasuk is an asmachta.
See moed katan (bavli) 3b and how they respond to R Gamliel uprooting an older takana.
R Akiva was more willing to make drashot that are not related to the p'shat meaning of a pasuk in order to provide a scriptural ground for a halacha, or change halacha than Rabi Yishmael. (Example with niddah, tefillin, theft of a goy). What is the power of a drasha? See menachot (bavli) 29b
What is halacha l'moshe mi'sinai?