the so called Hebrew calendar was never sanctified by any beit din. (If it was then this question would be a debate between the Talmud in Sanhedrin and the Talmud is rosh hashanah.) But as it stands today the Hebrew calendar is a mistake.
the great thing about Shulchan Aruch that even I with all my critiques on it have to admit is that a person that learns it generally has a good idea of halacha. While people that learn Rambam never seem to have the slightest idea of any halacha and don't even know what the very concept is.
Also it is important to understand the way the Torah is written. It was not meant to be taken literally. It is kabalistic. The apologetics to try to bring archaeological proofs to the exodus is wrong and unnecessary and also not true--and it goes against the very spirit that the Torah was written in.
Further it is important not to lie about these things. See the Ten Commandments and psalm 101:7 for further details.