I wouldn't underestimate the by now very experienced syrian army - the only insurgents are in the south, not counting the Kurds ("lol m8 why kill eachother look at all that free land ey"), but it'll have some problems
Now, samoa and the solomons won't stay in their current borders for eternity, not even a country full of downies would be that stupid, and in the same logic san marino no matter how small wouldn't immediatelly commit literal national suicide by refusing to claim anything (what switzerland gonna do, throw a fuss over 3 rocks and a hut when they have much better options)
Now the Saudis are screwed
The Syrian army was already well-trained and the only insurgent
controlled territory is in the south, there are still insurgents elsewhere. In the early phases of the war, it looked like the rebels were actually going to succeed in ousting Assad. His success comes with the backing of the Russian government, the fear Alawites have of reprisals, and liberal use of chemical weapons and barrel bombs in civilian areas, and even then the rebels have managed to hold together despite being a very diverse coalition. The sudden change in circumstances will not go unnoticed by would-be dissidents and those chafing under the regime, which is a lot of people. Similarly, those who depend on the Assad regime or benefit from it will not fail to notice the distinct lack of Russia in S world. The result of the sudden appearance of a great deal of no-man's-land and the disappearance of powers interested in limiting conflict to within Syria will result in the war expanding outward; the country is in too much of a stalemate, militarily and socially, to do otherwise.
I don't know what a downie is but you know that national borders don't expand for the purpose of filling map space, right? There has to be interest in actually claiming and settling new land, both on the part of the sponsor (presumably the state) and on the part of the settler. That's why people aren't dropping everything to go settle the Sahara as well as why the nations that claim parts of the Sahara aren't interested in rigorously enforcing their control of the region; the lines were drawn to prevent accidental conflict between occupying colonial powers and then they were just there. If you live in Samoa, the priority is ensuring that your family has enough to eat; for some people that will probably mean moving to what was once American Samoa. Otherwise, you stick close to the hand that feeds you, i.e. society. If there's famine, you might get some settlers trying to make their way to uninhabited islands but we've seen throughout history what happens when desperate refugees try to escape their situation by sea: it's never pretty. In any scenario, individual settlers that do make it to other islands and manage to survive their new environment will certainly not be tied to Samoa, which will be focused on maintaining internal stability and cohesion in a chaotic environment and unwilling to invest resources in more land that they can't manage. Ditto for the Solomons; there will be no great Pacific empires here.
And while we're talking about refugees, why not mention how it's overwhelmingly more likely for Syrian refugees to settle Italy than San Marino. 33,000 people is
nothing and San Marino is a country that has never, for the millenium and many centuries that it's existed, ever been interested in expansion. They literally can't manage to create a few pastoral communities even if San Marinese fascists took control of the country and mandated a policy dedicated entirely toward reproduction and settlement. Switzerland could twiddle its thumbs for a century and then move in and take Italy if it wanted; ditto for Spain, ditto for Senegal, ditto for Arabian and Syrian refugees and settlers. The most growth San Marino can hope to accomplish is to become an oddly-placed metropolitan center in a number of decades.