The Iranian regime looks to Syria as one of its key strategic assets. It will not allow the regime of Bashar al-Assad to fall without a fight. While it is difficult to ascertain the extent of direct Iranian involvement in the repression inside Syria, there are conclusive open source reports that the Iranian regime has been providing weaponry, financing, training, and perhaps boots on the ground through the participation of Hezbollah, which is an Iranian proxy, and possibly other forces inside Syria. The involvement of the Islamic Republic of Iran in supporting Syria's repression of its own people is significant and extensive.
As to the second part of your question, it is difficult to ascertain the Iranian public's awareness of events in the outside world. Iranians do have access to free information from the outside world. It is beamed inside Iran by various providers, based mostly in Europe or North America. However, the number of Iranian citizens who have the means to access these sources is rather limited. Not every Iranian is fluent in English. Not every Iranian is able to own the satellite dishes necessary to link up to these sources. The regime has been extremely active in trying to jam these broadcasts. Most Iranians get their news through government-controlled Farsi media. Therefore, their awareness of the extent of repression going on in Syria and the complicity of their own government should be questioned.
That is also true, incidentally, when it comes to the nuclear program. It is doubtful that ordinary Iranians are aware of their government's non-compliance with its own international obligations. They are probably not fully aware of the cost they bear every day because of the economic sanctions they suffer as a result of their regime's non-compliance with its own international obligations. They are not fully aware that their government is doing something that goes well beyond its legitimate right to have a peaceful nuclear program.