Before the Islamic conquest of Syria and the whole Levant, how popular was the Arabic language there? Are there any resources show what the percentage of Arabic in that region is as well?
To address Mark C Wallace's point, being ethnically Arabic and speaking the Arabic language are not the same thing. Arabic people existed long before the language we now call Arabic developed, albeit we tend not to refer to them as Arabic until the era of the spread of Islam and the Arabic language.
This is not a detailed answer, and it relies on Wikipedia (https://en.wikipedia.org/wiki/Syria#Middle_Ages). But for what it's worth:
The predominant languages spoken in Syria before the conquest by the Arab Rashidun army in 640 was Greek and Aramaic, reflecting the influence of the Byzantine empire and Byzantine Christianity. With the conquest, Islam became the dominant religion at the same time as Arabic became the dominant language.
The second part of your question I am unclear about. "Are there any resources show what is the percent of Arab in that region as well?"
Do you mean the percentage of the population that spoke Arabic before the conquest? Or today? Or are you talking about people of ethnically Arabic origin? If you are talking about medieval Syria, my guess would be 'no'. Detailed statistics for medieval history seldom/never exist. My best guess would be that Syria before the conquest was already ethnically 'Arabic' (except in this period what today would be called 'Arabic' was called Assyrian, Phoenician or Persian), but linguistically and culturally Byzantine. The Ghassanid Arabic group emigrated to Syria and the Levant in the 3rd century. In other words, the ethnicity that today we call Arabic, is simply the modern term for the same ethnicity that was called by a variety of names before the advent of Islam. After the conquest it became linguistically and culturally 'Arabic' too.
But I am far out of my area of expertise.
So in short, the answer to your question 'how popular was Arabic in the Levant before the conquest of Islam' is 'not very'.
Greek was the language of the ruling elite and Aramaic (or "Syriac") was widespread among the peasantry. However, Arabic was also widely spoken throughout Greater Syria, since there were many Arabic tribes in the area as well as in Iraq. Arabic inscriptions dating many centuries before Islam are found throughout Syria-Palestine, especially the southern parts. There were several Arab kingdoms as well, the Ghassanids (centered south of Damascus) and Lakhmids (of southern Iraq) being the last of these before for the Islamic conquests.