I would predict a 2nd Hungarian Succession war between Maximilian and Sigismund with Sigismund taking the crown of Bohemia.
Add in John Corvinus to that mix. He died in a post-battle plague outbreak on the Southern Frontier in late October, 1504. It's unlikely he would be fighting Ottoman incursions at this point in the given scenario. He would probably enjoy the support of the Újlaki(Ilok) and Frangepán(Frankopani) families.
He might actually act as the kingmaker though, standing behind Sigismund in a united front against Maximilian.
who would be top dog in that union and which culture would be dominant in court?
I think the Court would inevitably be located in Hungary, considering how crucial the quick travel of information was in regards to the Turkish threat. Not to mention, the shine of the Buda Castle was rather alluring. AFAIK, even Maximilian considered moving his place of residence to Buda had he managed to win the Hungarian crown.
Not to mention, despite the hardships it was facing, Hungary was probably still the strongest out of the four realms in question, which is another good reason for it to be the centre of the union.
And if the Court is in Hungary, then the simple matter of proximity would inevitably give an edge to the Hungarian culture in terms of Court presence. The union's real Lingua Franca would be Latin though, IMO.
2) With POD mere generation before Mohacs, Hungary is already in decline and Hungarians would be outnumbered by Slavs in Sigismund's realm by order of magnitude. And it is way easier for any Slav to learn Polish than Hungarian.
2) Was it in that severe decline? At the end of Matthias Corvinus's reign it supposedly had income rivaling France (tho I don't know if they counted also lands Corvinus conquered or not).
I wouldn't say Hungary was in decline per se. Under Matthias the incomes of the treasury from Hungary reached 900k Florins in good years and 600k in most years. Under the Jagiellonians, the usual annual royal revenues of Hungary amounted to about 300k Florins, or circa 500k if the extraordinary war tax was collected that year.
This might seem like the sign of extreme decline at first glance, but that doesn't fully reflect reality. The large discrepancy in numbers mostly come from differing approaches of governance. The Jagiellonians handled incomes in a less centralised manner compared to Matthias. This meant that they allowed the various polities/subdivisions of the Kingdom to retain more of their own revenues, providing them the means (in theory) to organise their defences locally.
Now, wether the Jagiellonians engaged in this type of governance by their own volitions is another question. I personally think it was primarily the product of circumstances. After all, prior to his stroke and then the tragic death of his wife, Vladislaus II was a surprisingly energetic ruler with a strong hand. Sure, the 1491 peace with Maximilian was humiliating (which was pretty much the cause of the Black Army's disbanding), but he proved to be very successful in subduing his domestic opponents. He tricked/outmaneuvred Beatrix, enlisted the support of Stephen Szapolyai and Paul Kinizsi, curbed the ambitions of John Corvin and suppressed Lawrence of Ilok. Even in foreign policy he scored a notable victory against the Turks in 1503. He achieved total peace for the duration of 7 years, when even the usual skirmishes and raids were (again, in theory) strictly prohibited. I also read a claim which I couldn't verify that even Szendrő/Smederevo was handed over by the Turks (then it was lost again in 1511).
Vladislaus lost his vigor in the second half of his reign and endorsed the abovementioned decentralised style of governing. This state of affairs was perpetuated by the infancy of Louis II and the regency council. Upon Louis' maturity however, things already began to develop in the direction of recentralisation IOTL, even despite the unpopular German-orientation and the crisis on the Southern Frontier.
Should Sigismund manage to secure the Hungarian throne in 1504-'5, I believe he would be more than capable enough to rule at least as effectively as Vladislaus did until that point.