I think Greater Poland and Silesia would had been absorbed to the Holy Roman Empire as a Rump Poland, the Vallachian principalities did not exist that time so a Mongol state in OTL Romania is possible since the Mongols could kick the Cumans from OTL Wallachia and Moldova.
That seems plausible, and probably the likely outcome.
Vallachian principalities (in the meaning of statelets) existed nevertheless, under Kuman domination. Not counting, of course, the Kingdom of Valachians and Bulgars.
Eastern Europe didn't look that strong at the time. The strongholds were of wood.
In eastern Poland and northen Hungary, yes. Not in Dalmatia, western Hungary, Croatia, western Poland and some part of Vallachia.
It was an easy game for the Mongols who could esily burn them down.
Not really, since the wooden strognhold appeared in Europe, you had plenty of tricks to not make them burn easily. Beast tides with water, equivalents of
murus gallicus (I don't know the english for "mur à poteaux frontaux verticaux" but it's the word in french for what existed in Eastern Europe), etc.
Of course, it couldn't really stand against an army in numerical advantage, but it's more due to the ability of such army to have siege engines rather than an inner weakness of wooden strongholds.
A raiding force or a small expedition, admitting it have interest into besieging all strongholds (that is not really likely) would have to use the good ol' siege and wait the ennemy to be starving.
Stone cities in eastern Europe begun suddenly apearing soon after but wth the actual Mongol raids there was none of it.
And? Many wooden strongholds fairly resisted the Mongols (not talking of stone fortification in Croatia/Dalmatia, as well western Poland that existed).
Having a stone wall isn't a magical feature, when wooden fortification are useless. I stand my point : Mongols weren't able to take control of the country because of a coherent and strong net of fortification, more stone in the south and west 'as in Klis stronghold in stone since the early XII maybe earlier, at least before the Mongols arrival), more wooden in the north and east.
Wooden strongholds weren't really a "how my god we forgot that wood can be fired!" feature. It was a cheap, efficient way to fortify with limited ressources and that was often coupled with a limited use of stone (as stone fortifications up to the XVI used many wooden features).