We want to know if Arabic is the root of all spoken languages?
Arabic is one member of the Semitic family of languages, which itself is a branch of the Afro-Asiatic superfamily. The earliest evidence of proto-Arabic or Old North Arabian, the earlier language that was the ancestor of classical Arabic, dates back to around 1000BCE, about the same time as the emergence of Aramaic and Ge-ez which are also Semitic. Other Semitic languages are older, such as Old South Arabian and proto-Canaanite (the ancestor of Hebrew), all of which date to around 2000BCE. Proto-Semitic, the reconstructed ancient language from which all of these are descended, is thought to have become established in Arabia around 4000BCE.
The Afro-Asiatic superfamily also includes ancient Egyptian and the Berber and Cushitic languages, among many others.
As for there being a single ancestor for all languages, that is a very controversial topic. We have established a number of language families and superfamilies in addition to Afro-Asiatic. Indo-European includes most of the languages of Europe plus India and Persia. The Mongolic superfamily arguably includes the Finno-Ugric, Ural-Altaic and Turkic families as well as Mongolian, Manchurian, Korean and Japanese. There are three aboriginal language families in the Western Hemisphere corresponding to the three waves of migration from Siberia in 14000BCE, 6000BCE and 4000BCE. There's Malayo-Polynesian, there's Sino-Tibetan, there's a family of languages in Australia and New Guinea, one or two in southeast Asia, and a few isolates that defy categorization like Basque and Georgian.
But some linguists hypothesize that all languages outside of Africa are indeed related, and tantalizing evidence has been found by massively parallel computers to support this hypothesis. Unfortunately there aren't enough correlations to be certain that we've found fifty cognates in all the non-African language families, or merely fifty coincidences among tens of thousands of words, which does not quite defy the law of averages. Nonetheless if this hypothesis is true it would indicate that the diaspora of Homo sapiens out of Africa in 70,000BCE brought a single language with them, and it has diverged into what we see today. It would also prove that the technology of language itself is at least 70,000 years old and might be the key technology that permitted us to perform the planning and organization necessary to successfully migrate out of Africa.
What evidence is there for or against?
To answer your shorter question, there is abundant evidence that Arabic is merely one member of a language family, and in fact a relatively new member. The earliest language related to Arabic that we have hard evidence of is Akkadian, which was spoken in the Babylonian Empire a couple of thousand years before Arabic sprang up.
Then Sanskrit is the root of Latin and Greek. You would have to look it up but I think there are several braches even before Sanskrit.
Sanskrit is the ancestor of the Indic languages but it is a contemporary of Latin and Greek, not their ancestor. The tribe that lived somewhere around Anatolia or the Caucasus and spoke proto-Indo-European split into an Eastern and Western Branch around 4000BCE.
The Eastern Branch is the source of the Indo-Iranian languages, the Balto-Slavic languages, and several others such as Armenian. It was once called the
Satem branch, named after the Sanskrit word for "hundred," because the K in the Indo-European word
kmtom for "hundred" becomes S in all of these languages, such as Russian
sto.
The Western Branch was called the
Kentum branch, named after the Latin word (spelled
centum but the C was hard) because the hard K was preserved in the ancestral languages of this branch. This naming convention has fallen into disuse because the K has dissipated in the modern descendants of those languages except for Greek
hekaton and Gaelic
cead. It became H in English
hundred, CH in Italian
cento, TH in Spanish
ciento, S in French
cent, etc.
Latin and Greek are Western Indo-European languages (as are the Celtic and Germanic languages and Albanian). Sanskrit is an Eastern Indo-European language. When early European scholars first discovered documents in Sanskrit they were struck by its similarity to Latin and Greek and realized that there was such a thing as an Indo-European language family. Not knowing the chronology of the documents very well, some of them assumed that Sanskrit was an older language and could be the ancestor of Latin and Greek, but we now know this is not true.