Firstly, Hebrew is similar to Arabic because they are in the same 'Language Family' the Semitic family. (Who's ancestors are believed to have lived in Ethiopia at some point, before bypassing Egypt and starting life in the Arabian peninsular and later spreading to Mesopotamia and Palestine etc.
'Older'? As I understand it that's almost impossible to determine, there were speakers of Semitic languages long before there was any method of recording them at all, saying which is older isn't really possible, especially since they both evolved from one language at one point, and the definition of 'dilaect' of the early Semitic language, and seperate language from it is a mater of conjecture anyways.
There are PROBABLY older writings in Hebrew than in Arabic.
Similar - both semitic, most words come from the same roots, although I believe Arabic will have more foreign loan words, since when Hebrew was resurrected as a spoken language the resurrectors decided to import no foreign words, even for modern devices, I think a television is called an 'angel box' to avoid importing words, although you may want to check that.
The most obvious difference is their writing system, Hebrew uses a modifed alphabetic script, whereas Arabic uses a native script for writing. Hebrew is also written left to right, not right to left, since when the Israelis borrowed their writing technology (which came ultimately from the Phoenicans another Semitic people) they imported over ideas from them aswell.
They will have evolved differently because they were geographically isolated from one another, in comparison the Seimtic language used in Mesopotamia before Aramaic (which was the language Jesus would have spoken coincidentally), eventually splintered into different languages within a thousand years. Vulgar Latin also evolved into the romance languages in a similar length of time, Spanish, French, Portugesse, Romanian, Italian etc.
According to a book I read 'language history of the world' Semitic languages have a similar grammar, so Hebrew and Arabic would be grammatically similar to Akkadian (and later Aramiac) the languages of Mesopotamia, this grammatical similarity (along with shared root words) is why Arabic is spoken to widely across the middle east, virtually everywhere that currently speaks it spoke anohter Semitic language, some have said that all a person would have had to do would be to learn different words (which would be fairly similar) and eventually the Arabic words and concepts overtook the Aramiac, Syriac (a form of Aramaic which developed into a seperate language within a few centuries of seperation) languages there already.
Hope this helped things.
I recommend reading about langauge families and evolution if you're interested.