Alright Personal answer as many do not seem to know too much about Syria, myself included, this may be a bit long
For reference in this answer: The current Syrian Constitution
To start we need some history
Syria was under French mandate from 1922-1944 effectively giving them control over Syria. After the French had withdrawn, Syria has been in a constant state of civil war with one coup after another with factions constantly fighting, some even sponsored by the US. The regimes went through many different periods of dictatorship and democracy's constantly being replaced.
It was not until 1963 when The Arab Socialist Resurrection (Baath) Party (hereafter, Baath Party), with a secular, socialist, Arab nationalist orientation, took decisive control in a March 1963 coup. The Baath Party was active in throughout the middle East since the 1940's.
In 1970 a revolt occurred after many military failures a bloodless coup occurred and Hafez al-Assad, former Defense Lieutenant General, won the popular referendum and became president for the next 30 years.
In 1973 a constitution was established defining the roles of parliament, the president and vice president, the cabinet of ministers, and the people. It began by declaring Syria under a single party system that party being the Baath party, Islamic Jurisprudence was also established based on Shia law, the president is also required to be a follower of Islam. However, it also allowed for freedom of religion so long as public order is not threatened, this would later be used primarily on Sunni Arabs and Jews in Syria. There was a large focus on education and jobs as a right of the people for the government to uphold.
During the next 30 years Hafez's regime would be labeled authoritarian as a State of Emergency was declared allowing for suppression of citizens. Notably the Muslim Brotherhood who rose up declaring the regime too secular, I honestly didn't think I'd be typing that. Many reports of people disappearing or being assassinated. The economy also did poorly during much of this time according to the source in the header.
In 2000 Hafez died. Parliament amended the constitution lowering the age for the presidency from 40 to 34 allowing Bashar Assad, Hafezs son, to run. Parliament did not elect any opposition to run against Assad.
Assad was met with pushback. A few years later Assad began reforming by enforcing/enacting mandatory retirement and replacing certain high-level administrators with appointments from outside the Baath Party. This effectively kicked many of the old out of the government who opposed his rule.
In 2011 many rebellion groups began to pop up and a few years later a civil war broke out.
In 2012 the Syrian Constitution was amended again transforming Syria into a multi-party democracy like much of the West.
It can be for 3 months. Syria follows a parliamentary system. In this system The Citizens of Syria elect members of parliament who then proceed to nominate one or more candidates for the presidency. The president then appoints a cabinet who have to be confirmed by parliament, the same way in the US.
The president more or less has power over most things aside from the law, which he is tasked to enforce. When parliament is out of session the president gains power over the law, however when parliament is back in session their first order of business is to scrutinize any laws made with the ability to throw them out in their entirety.
The president can also abolish parliament for up to 3 months, however a reason is needed and parliament can never be abolished twice for the same reason.
The president also has veto power, when parliament passes a bill the president can veto it, in which case it goes back to parliament where if it passes again with a super majority it will become law.
So in short, kind of. The president can gain absolute power at times and the system is flimsy without much oversight that I could find of the president itself. I'll put it this way if the US is a Demo-Republic then Syria is an Oligarch-Democracy.
Also worth noting in the 2012 referendum the presidency was limited to two 7 year terms. Meaning that if they wish to prove any semblance of non-dictatorial rule that this should legally be Assads last term ending in 2021. One more thing, a state of emergency had been in place for over 30 years allowing governments to seize those that speak out openly against the government. Assad lifted this state of emergency in hopes of avoiding a civil war.
The Syrian regime, under the founding Baath party, seemed to show a great deal of French influence with their political breakdown/separation of power, religious liberty, and the government giving to the people. These were not commonly found during that period with many still being under Shariah or totalitarian regimes.
Not to say this is not a totalitarian regime. Syria had been in a State of Emergency for over 30 years now suspending many of the citizens rights, which rights I cannot say. This allowed the ruling regime to crush the opposition brutally. The current regime have lifted this state of emergency in 2011 in hopes of .
Religious Freedom is alive in Syria, however you might end up being monitored or arrested depending on if the government deems you as a threat or radical. So unless you believe what the government believes you do not have a guarantee of safety, but yet again this appears to be widely focused on Islam and I am having trouble finding instances of Christians being brutalized, though Jews are widely discriminated against, although there are systems in place to protect them (Jews in Syria). That being said I have no basis on whether the Arabs persecuted were radical so please take that with modicum of salt I am merely basing that on the crackdown on the muslim brotherhood and the general tone of the area arguably/in-arguably discriminatory, but this is the thoughts section, always open to read new sources.
Speaking out against the government was also banned, I am assuming this has to do with the State of emergency. Doing this seems to get you jailed according to the sources and this seems to be a main stay of the current political asylum seekers from Syria, though having trouble finding examples of political asylum seekers and why they are seeking.
Syria for the area seems very progressive for an Arab nation in that region. Although I am not comparing it with it's Israeli neighbor Israel but if you view Religious Freedom is alive you can see that few other arab countries in that area tolerate any other religion. The reformations under the current regime are also very positive as it is no longer a single party system.
Criticism is simply that the State of Emergency made the rights questionable and gives the government far too much reaching power by Western standards. The disappearances and brutal suppression of those that speak out against the family or government is also very disheartening. We cannot forgot about the abuses of power such as redefining the constitution in 2000 for the sake of what amounts to a Kingdom/Monarch. The president is also a pure dictator while parliament is out of session as he gains the ability to make and enforce laws, those laws are reviewed as top priority when parliament reconvenes but it appears to be far too much power. State of Emergency has been lifted since 2011 with hopes of the regime putting a better foot forward though alleged reports of abuse were still prevalent since then
Now for the war - and not the inevitable comment war
In short the war is MUCH bigger than I thought Factions fighting in Syria.
It seems the only role the US is supporting is The Combined Joint Task Force, however this is purely against ISIL. We are providing arms to various groups as well, however we do not seem concerned with their ideology as the Syrian Democratic Council has ties to ISIL, though I cannot comment on the stretch. The Syrian opposition is funded by Qatar who are having some issues lately due to funding radical groups. I do not mean to be too dismissive of these groups, however there is very little known about what they want so all there is to go off of is association. That being said US's reasoning for arming these groups would be an entirely separate question altogether
Please bear in mind this post is not to make any types of excuses or promote any belief. If you disagree with something and have something that will change my mind please feel free to comment.
Also please note the history source has various comments to party suppression, however to reiterate a point in the answer, it was in the constitution that the country would be single party that is until 2012 when they removed Article 8.