Played a bit and I think it's a very solid start to a game, given it's still in alpha.

Based on what I've seen I don't know whether there will be anything to determine the style of government/senate/political parties. It would be great if it has, as I like to see some the 'internal' political aspect  (I enjoy the 'external' aka Diplomacy too) but rarely found one with a good depth. I think its a good addition to the game that can add a level of challenges, especially to the big dominating empires. Here's my 2 cents (if not happenning, please ignore this, I just like to get this off my chest)

Rather than cookie cutter government structure (republic, democracy ...), I suggest it can be controlled by levers (policies decisions/legislation)

• Constitution - when the game start, you draft a constitution (or one if give that tailor to the race) and it sets out
• What are the organs of government and how power is shared among these organs
• executive 
• you/the player
• are you able to directly influence (direct the members that are 'appointed' by you on what and how legislation parliament will enact)
• can you dissolve parliament
• can you fired judges (see judiciary/court)
• can you declare martial law/state of emergency 
• can you veto legislation (is there decision that you can't veto)
• parliament/senate - approve legislation that can support or oppose your decision depending on whether it is favourable (can be favourable, unfavourable or hung parliament)
• how each planet is represented (how many members per planets)
• how many for the home planet
• how many for other planets
• calculated per population or just a set number?
• how is it elected/appointed (or what percentage are 'appointed')
• the more elected officials as a proportion, the more happier the population is, but can be less stable, at worst, uncontrollable
• how long is its term (e.g. election every 10 turns, unless you dissolve it)
• what is its capacity (amount of legislation it can process per sitting, e.g max 5 pieces per sitting)
• is there certain race/people you block out (to discriminate)
• is parliament consent needed to go into war
• can it stop a war
• can it block a trade deal/treaty
• you can act against the parliament and its legislation but you may be taken to court (see below)
• judiciary/court - can penalise the player for actions that is illegal and/or unconstitutional
• is the court independent
• how many judges
• are you able to stack the court to your favour
• if you have high enough influence and the court are independent enough, it may act as the 'galaxy' court that can resolve disputes between other races/players and issue penalty (with a fee)
• How/if the constitution can be amended
• Over the course of the game 
• the Constitution may be changed as society and technology advance
• if there is no mechanism to change the Constitute (at least the part you want to change and there should be parts that are locked away from the start), you are given the option to start a 'revolution' to reset the Constitution; everything that your technology and society allow are made available to you.
• Revolution can cause chaos and damages to your planets, it also increase the risk of planet that has low attachment to break off/join others during that time
• Some race may be more resistance and recover from revolution faster (population size can also be a factor)
• executive
• there are levers policies for you to set within the limit of you technological advancement and racial attributes (impact of a decision maybe different between different race). here are a few concepts
• labour union: 100% <=> 0% (some race may benefits from union involvement, some race won't)
• environment: Full legislative protection <=> market mechanism <=> no control
• you can act outside the legal bounds, but you may be penalised by the court
• parliament/senate
• Sit regularly (e.g. one per term or per every 3 turns) 
• enact new/amend and existing (a pre-set volume of) legislation (see constitution above)
• in regular sittings you have no control of what being tables in parliament (you do that in emergency sittings)
• they will be first bring to your attention as ask for your comments
• you indicate what your decision is (make a choice out of 3, input a number if required or just simply yes or no (like whether to approve a trade deal you've made))
• or to boycott it; with enough numbers, it may not get on to the floor for a vote
• Then it will go to a vote
• if there are member who are appointed, they will (very very) likely to vote as per your wishes
• favourable members will likely to vote with you
• neutral members may to vote with you (depending whether they owe you any favours, see below) or abstain
• opposition members will unlikely to vote with you (but they may still vote for you if they owe you enough favours or it's in their interests)
• you get a decision 
• if a stalemate then no decision: some actions may need the law changed. (e.g. you may not build heavy polluting industries which gives off huge production if the environmental standards remain high, which you want it lowered; no decision means you can't build it) 
• if you want to change the decision (or gets a decision) you can veto it and send it back for a second vote.
• this time, you do some shadowy stuffs, such as bribing, assassinate or stronger arm twisting. 
• No abstaining in the second vote (but if caught the court may void the decision, as least will impact on the voters)
• You get the cast the tie-breaker vote
• Can call emergency sitting, such as to declare war or change a piece of legislation that suit your needs
• member don't like emergency sitting, unless it's an emergency (namely going to war), so there's a penalty on whether they will vote favourably
• members may seek you to ask for favours (build a entertainment facility at his/her/its planet or just a 'political donation'), they may return the favour later.
• elections
• depends on whether the voters are happy (or you simply oppress... i meant impress... them enough)
• maybe you can make election promises (end the war, create jobs, clean the environment ...) which you are being hold to
• big achievements earn points
• new parliament won't swear in until the next turn
• you can dissolve parliament when you like, but vote may get voter fatigue over time. 
• All laws enacted remains until they are amended or repealed, parliament will revisit the old ones to ensure they are up-to-date 
• Nonetheless, unless specified in the Constitution, the decision from the parliament is to set boundaries to your actions (policies and decisions), not to prevent them (if it is available to you, then you can act on it legally or not). it is for the court to decide one the punishment if it is illegal. In other words it shouldn't have great impact on on the game play (unless you specified in the beginning when you draft up your Constitution) rather more dilemma to consider.
• judiciary/court
• if you have 'control' over it than you just tell them what decision to make.
• if it is independent, you are given a chance defence yourself through a serious of questions. the judge will make its ruling
• if the decision is unfavourable, then you can appeal the decision which you are given the opportunity to do your shadow stuffs; or adjust your action to make it legal. 
• decision won't be made immediately, you may have a few turns to take advantage on what you are doing. (unless you have control of the court)
• nothing stopping you to readjust it back to illegal, you just get challenged again, repeated offender will be punished harshly
• the harshest decision is to remove you from power for a few turns.
• Other notes
• in espionage, you may able to plant spies in as a member of parliament and/or judges. 
• You can influence a lot from labour condition to trade deals to going into war.
• With clever moves, small empires can cripple larger one through political influences
• On a broader note, in Diplomacy
• it may be fun to form 'blocks' that fall under a "United Planets" (if it exists in this game) like NATO, APEC or ASEAN. That draw closer relationship.
• I think its size should be limited no more than 1/3 of players and NPCs, so that it won't dominate the United Planets
• You build up a standing/reputation within the organisation, they highest will become chair and heavily influence trades, issuing emergency relieve programs, assisting members or joint research programs or joint production facilities or resolving disputes between members
• standing/reputation
• your overall 'power'
• can be increased by contributions to the the pool of fund that can be used as disaster relieve
• can be increased by assist others in need
• can be increased by your vote in the United Planets aligned with others in the block
• can be decreased by exposed spies
• etc etc
• depending on the winning conditions, you may need to win alone or as a block.

This is probably too complex to work, but I just want to get it off my chest. Hope it still got a bit of merits.

Thanks for you time.