Is Iran really internationally allowed to go at war outside of Iran?
Yes Iran is a sovereign state, it is bound by exactly the same rules of war as every other nation, that is either being authorised by the UN security council or being invited into the country by the government of that country.
Iran has only been involved in Syria with the support of the Syrian government of Bashir Al-Assad, as such have a legal right to be there.
It is worth noting that the US has neither a UN security council resolution or an invitation from the Syrian government, so technically it's America who is breaching international law by being in Syria.
It's also worth noting your first statement about
The Iranian regime actually is at war outside Iran
Is unsupported by the article, as it only says an Iranian made drone was used in Syria. US weapons are used in Yemen, but that does not mean the US is at war in Yemen. It is true however that Iran are involved in the Syrian conflict, but this is not correct evidence
As to you second point
Does America have a serious plan to deal with Iran? or Iran will be out of control Like North Korea?
This is completely subjective and opinion based, the US government does have a legitimate strategy in Iran, just like it has a strategy for every other country it deals with in the world. Whether it is serious is subjective and your other implied point about either Iran or North Korea being "out of control" is also subjective.