The "tribunals" are arbitral tribunals and as such are manned by lawyers chosen and agreed on by BOTH sides - just like any other arbitral tribunal. They can apportion compensation for damages caused by breaches of international law. No international court can "force" a state to change a law (this is constitution 101), and it is not the case here.
Philip Morris is seeking compensation for the purported expropriation of intellectual property rights (their brand). Almost no-one believes they have any chance of winning. In fact, it seems that they are doing it solely to press for time in other jurisdictions: i.e. some countries are waiting for the result of the arbitration before introducing similar laws. They probably figured out that potential lost profits in foreign markets in that time frame are likely higher than legal fees.
Not one of your points is accurate (and you reference John Oliver and a comic).