First off, it's important to establish that a sense of modern nationality and nationalism didn't really exist within an early modern entity such as the Polish-Lithuanian Commonwealth. Today's markers for "nation" (ethnicity, religion, language, citizenship) had the potential to be much more fluid in the early modern period. Therefore, conceptualizing the Commonwealth of as two separate nations obscures the complexities of this political and social arrangement.

The precursors of the union were the personal dynastic unions of the fourteenth and fifteenth centuries. Both the threat of the Teutonic knights and Muscovy allowed the Jagiellonian dynasty to expand its influence both among the Lithuanian and Polish nobility and gentry. The 1569 Union of Lublin was the culmination of these efforts. It created an elected monarchy (not that uncommon in the early modern period) and a common diet (which was unique- its nearest analogue, the Anglo-Scottish union came 138 years later). The Union actually worked against the interests of the Jagellonian dynasty. Lithuania and Poland both retained a separate army, administration and legal system. The national diet acted as a check on royal influence and further confused the question as to where exactly did executive authority begin. Power was often shared in a tenuous triad of royal authority, magnate interests, and the hereditary nobility. Culturally, the Commonwealth was characterized by a degree of cultural hybridization; Lithuanian nobles frequently spoke Polish as a language of culture and adapted to Catholicism.

The clunky political organization of the Commonwealth put a ceiling upon the power it could exert. Although its territorial expanse reached its peak in 1619, the expansion proved fatal for the long-term health of the Commonwealth. As it expanded into Ukraine, it could not replicate the roughly equitable relationship between Lithuanian and Polish elites that had sustained the Commonwealth. The diet prevented the accumulation of a fiscal or a military base which early modern states increasingly needed. The expansion also brought it into conflict with both Sweden and the Romanovs. As pressures mounted, the diet and elective kingship proved to be counterproductive to efforts to shore the Commonwealth up. Although the Commonwealth achieved a few successes, such as the 1683 relief of Vienna, it found itself increasingly on the defensive against its neighbors.

Sources

Frost, Robert I. After the Deluge: Poland-Lithuania and the Second Northern War, 1655-1660. Cambridge: Cambridge University Press, 1993.

Snyder, Timothy. The Reconstruction of Nations Poland, Ukraine, Lithuania, Belarus, 1569-1999. New Haven: Yale University Press, 2003.

1. both Poland and Lithuania were threathened by new growing power - Teutonic Order so the Poland have choosen Lithuanian from ruling family as a Polish king to make alliance. It was peaceful and took a long time - at first it was personal union, then it changed into closer and closer alliance, and eventually they merged into one federational state in Lublin Union (and eventually it turned into more integrated state in 3rd May constitution, but that was the last effore before final 3rd partition of Poland, it only lasted a few years - for most of the time it was federation).

2. Poland was the stronger side, not because of the law (it was quite fair), but because of cultural assimilation - Ruthenian and Lithuanian leaders and important figures were recognized as nobles in Polish law, and they quickly polonized. Lower classes kept their separate cultures, but the power was in hands of Polish and Lithuanian/Ruthenian nobles.

Some of these nobles become magnates, owned land bigger than many countries, and had sometimes bigger influence than even the king (see Radziwiłł family from Lithuania, Zamojski family from eastern Poland, or Wiśniowiecki from Ukraine). So it's hard to clearly say who had the bigger influence - depends on how you measure and when.

The important decisions were made by voting (each noble had the right to do that - around 5-10% of male population), votes were often bought by magnates or foreign emmisaries, so each voting session could have different factions with different distribution of power depending on who bought more votes, who declined to be bought, and who skipped the session altogether.

3. in the first league, but not the biggest power. It had one of the best armies in region, with cavalry that repeatedly won against pike infantry units outnumbering them 10 to 1 or more, but it had small army for such a big country, because the taxation level was very low in the Commonwealth (nobody votes to increase taxes on themselves), thus it had small king-controlled army, and many magnates-controlled private armies and mercenaries bought as-needed. It was land-only power, and it was often paralysed by the voting system. For example often when king wanted to use army he had to promise something to the nobles so they accept the taxes/go to war with their private armies.

How did Jews fair in the Commonwealth compared to other areas of Europe?