How does the New Intergalactic Imperial Republic work?

That's not an easy question to answere. First of all, it is important to remember that the NIIR is a group with it's roots in the NI (New Imperium). From there, they got a part of their name, the New Intergalactic Imperial Republic. The (Imperial) President got the Emperors role, but he hasn't the power an Emperor would achive.
The parlaments name is The Group. The Group is the 5 highest NIIR members and the President. The president can dissolve The Group and put together a new one. The Group in turn can dethrone the President. But they must hold a voting among the members in NIIR with 70% saying that they want to chose a new president.
The ranks that gain a post in The Group is: The Warlord (who also is vice President), The Economy Advicer, The Intelligence Commander and the two Admirals. If there aren't enough members to fill this ranks, the President and those of these ranks there are filled will regin the Republic at equal connditions.
The President got the fully responsability for everything The Group does. Therefor he got veto in the Parlament. It's praxis for the President not to use his veto.
If the President use his veto, the President have to make an own proposal in the issue within 96 hours, or four full days. If the President fails, The Groups proposal will go through. It's here the President may want to dissolve The Group. This can lead to lost confidence in the Government.
If The Group is dissolved the members will lose thier ranks to members that the President chose. This is not the case with the Intelligence Commander, who will be executed within 24 hours. The new Group will be chosed by the President, if he not let it become an election issue. The five posts have to be replaced within a week.
All this can be change in the future if that change is approved by both The Group and the President.
And please, the most important of all: Have fun!