Out of all of it, I'm wondering, what are the major pro's and con's of
abolishing the idea of 'nations' and becoming an intergalactic nation
Governments are based on violence, that's what they do, they how they function. If an organization cannot enforce its decisions by violences, it's by definition not a government.
History is pretty clear that when government lack external threats or competitions from other governments, they turn their capacity for violence on their own people. Perhaps more accurately, the subpopulation that comprises the "government" uses violence to oppress and exploit the rest of the population. Tokugawa Japan is a crystalline example, although any of the large pre-idustrial empires will show the behavior as well e.g. the Roman Empire fought more Civil Wars that external wars as did most Chinese Dynasty Empires.
History is likewise clear that such Empires value stability and stasis over change or progress of any kind unless forced by outside pressure. Tokugawa Japan did not advance or change at all for nearly 250 years. Likewise, the Ottoman Empire froze itself in mid-1700s for nearly 150 years.
Any kind of "World Government" established before contact of knowledge of possible alien competition would shortly turn tyrannical, murderous and static. Likely, such a regime would never foster space travel as it would view it as far to destabilizing.
Conversely, most progressive civilizations shoot ahead of their peer civilizations when some crisis, quite often external military, forces the society to become more merit driven and egalitarian to survive. Golden Age Athens, the Roman Republic, Venice, the Dutch Republic, Meiji Japan etc. We also have the example of formally squabbling local polities uniting against exterior foes e.g. the Greeks in response to the Persians, Italian states in response to the Celts, Daimyo clans in Meiji Japan in response to contact with the rest of the world.
The best case scenario would be the world remaining dividing into competing polities until after contact with aliens occurs. At that point, a unified world government, more precisely the subpopulation with the powers of the state, would have to take into account the aliens when making policy. If they made earth culture to static, they aliens might out develop us in technology or spread farther.
It's worth noting that historically, long distance trade, exploration and colonization were also powerful drivers of meritocratic and egalitarian societies. When people found themselves thousands of miles away from home on the seas, or having to trade with distant peoples or stuck out on a frontier with help weeks or months aways at best...suddenly they stopped caring "what" or "who" an individual was based on the traditional culture and just started caring about what real skills and benefits they could bring that would help the community.
The people on colony worlds or traveling in space would very quickly develop a different culture than their parent cultures on earth.