As for the similarities, there is nothing strange because both Hebrew and Arabic belong to the Semitic language family. You can find even closer lexical similarities between English and German, Russian and Serbian, French and Italian, etc.
Many years ago, when I was but a lad, I brought this up with a rabbi in Jerusalem. His answer was that "Lashon haQqodhesh" does not mean "Hebrew" as we know it.
Lashon haKodesh is Hebrew. The rabbi meant that modern Israeli Hebrew is very simplified, both in grammar and in phonetics.
I suppose one could say that Lashon haQqodhesh was what some would call "proto-Semitic".
This is wrong. Even though Arabic and other Semitic languages are close to Hebrew, you cannot extend the concept of Lashon haKodesh (Holy Language) on them. Witten Torah was written in Hebrew, not in Arabic, Aramaic, Ammonite, Moavite, etc. (and it was written for the Jews but not for any of these peoples). Torah was given to the Children of Israel (bnei Yisra'el), not to the children of Sem ("bnei Shem") in general!