The Mongols lacked siege engines when they first rolled into China, but they quickly conscripted Chinese siege engineers from conquered areas and used them. The Mongols were very good at recognizing who would be useful among conquered peoples and conscripting them. If the conscriptees did good work for the Mongols, they would be rewarded.
China was full of stone fortifications at the time. Fortresses and fortified cities were common in China and the siege engineers were among the best in the world.
After the Mongols begin expanding elsewhere, they took their siege engineers with them. Central Asia, the Middle East, Russia, and Europe. Fortifications weren't a problem for them.
The Mongols weren't bothered much by a lack of plains. Their horses were hardy and could survive on what was available.
The Mongols strength wasn't that their warriors were so much better individually. An individual European knight was much harder to beat than an individual Mongol. It was that they worked very well together. Their teamwork and discipline was unprecedented, and their lack of a supply train, their excellent mobility, and their incredibly good coordination allowed them to attack from multiple directions simultaneously. They struck where they weren't expected and could ride circles around other armies.
Their ability to divide and conquer their enemy was also very good. They'd take advantage of divisions in their enemy and exploit them. They turned the Hungarian people against the Cuman horseman who had fled to Hungary, depriving Hungary of large numbers of steppe horsemen.
The Mongols drove deep into Europe during their conquests, devastating Poland and Hungary, and making it as far as eastern Germany. The only thing that ended up saving Europe wasn't Europe's political system, fortresses, knights, or feudalism. It was the simple fact that the Mongol khan had died and the Mongols turned around and went back home. Europe would have been toast otherwise. The Mongols had far larger military forces at their disposal and the brutality to keep their conquered peoples in line.
They never made a concerted effort to conquer Europe again, although they dominated Russia (including the heavily forested areas) for centuries. They used conscripted Russians against each other as well, so often the Mongols themselves didn't even need to get involved to keep their lands.
Interestingly, at the Battle of Mohi, the Hungarian army managed to hold on against the Mongols for a while when they were both fighting at close quarters across a bridge. With fighting like that, the Mongols were at a disadvantage.
The Mongols got tricky and attacked the bridge during the night, and bombarded the Hungarians with all sorts of artillery. There were explosive devices used that night, and some historians speculate that there could have been gunpowder used in that battle. It also could have been just burning pots filled with flammable material. The Chinese did have gunpowder at the time, although it wasn't being used for guns, so the Chinese engineers may have used it.
At any rate, that whole attack was just a diversion. The Mongols had also crossed the river during the night, and when morning arrived, the Hungarians were surrounded. The Mongols left an escape path purposely, prompting the Hungarians to start to panic and run through the gap in the Mongol lines. Then it was easy to chase them down and kill them. European knights are a lot easier to beat when they have flung away their armor and a fleeing in panic.
The Mongols may not have been the toughest individual warriors around, but their trickiness, teamwork, brutality, and ability to make up for their weaknesses with skilled conscripts got them very good results. The army that wins isn't always the toughest one, but the one that doesn't panic and run.
If anyone's interested in the Mongols, I recommend listening to some older episodes of Dan Carlin's Hardcore History podcast. He had five two-hour episodes about the Mongols that were very interesting and well researched.