I take it as a sort of a pun, as is not uncommon in titles of this sort in an attempt to attract interest. Yes, the word "quarrel" usually describes a personal altercation rather than conflict at a national or international level. Often the quarrel is between two parties who have some sort of existing relationship, such as colleagues at work, or husband and wife -- a sadly not uncommon occurrence which gets its own term, a "domestic quarrel". But the word "domestic" also means a country's home affairs as opposed to its international relations, e.g. "gross domestic product", etc. Here the word is to be interpreted both ways to describe a civil war -- appropriately or otherwise, I will leave you to judge.

A quarrel is typically petty, usually between two people. A feud is generally between two larger parties (like two rival families or gangs). Strife is the ongoing feeling of a long and arduous battle or series of fights. Toward or towards is correct, depending on where you live and what you prefer. Syrian would be capitalized.