This is a intresting question.

The Mongol conquests steamrolled over many theatres, ranging across China, Manchuria Korea, Central Asia, the Middle East, Russia, Eastern Europe, and all lands in between.

First of, only some of those places are in the scope of the questions, the conquest of ruissa and some of the other places only happend after he was allready dead.

Ghengis threw his hole life comanded personally whenever possible, at least as far as we can tell. He was with the main army pretty much all of the time. We can of course not say all that much about the unification of the tribes but from all we do know this was the same there.

Did he travel with a personal elite army or did he simply take command of whatever army was already on the scene?

Ghengis had a personal tuman, that kind of function as a combination of bodyguard and general staff. He did not really travel from army to army with this tuman but rather, he would always move with the main army. So usally with Ghengis travelled more then just his tuman.

When Genghis Khan was not present, were his generals using military doctrines and occupation policies devised by the Khan himself, or did they each have their own style of conquest?

Genghis promoted people based on two things, personal loyality and skill. As far as we can tell, comands to his trusted generals that where able to operate without him, where very broad and gave a lot of freedom to the generals. This is one of the major reasons for the success of the mongol army, the could manage multible large field armys that operated complelty independed but still able to work together. It was won typical mongol strategy that they move about very away from each other but at the decisive point the would fight together again or alternativly fight by themselfs for years at the time.

We dont have enougth detail information about planning of campains or know enougth about the orders he gave his generals when he left them in some place.

Now maybe lets look at some example, so Genghis got himself into a war with the Sha while he was still active in china against the Jin. The distance from Genghis 'capital' to Samerkand was gigantic and the effort for a offencive was huge. At the same time he could not leave the Jin to reconquer everything. So what he did, is to leave behind one of his most trusted generals (Muqali) and himself went into the west for multible years. In all this time Muqali managed to take more of northern china and he stayed loyal. Muqali is not one of the well known mongol generals just because he died relativly early but he must have had a huge amount of trust from Genghis. He also proved his ability in china. So here we see the typical operation of Ghengis, move with the main army and leave a smaller but still large field army with a good personally loyal general.

Another good example is when Subadei and Jebe followed the Sha deep inside of enemy territory all the way to the caspian sea. Know at this point the had done pretty done all they where asked to do. During there campain the operated with minimal guidance, after that however Genghis order Subadei back to him. This was acomplised with unbelivable speed, Subadei got new orders and was sent back to his army. From then for the next couple of years Subadei and Jebe operated completly indepenedly again.

Field armys not lead by Genghis himself for the most part where about as effective as with him, meaning very effective. The reason for this is that bot on high and low places of leadership, skill was required to move up. On low levels there was some democratic promotion, on high level, personal loyalty and skill. This is very importent, even personal friends and familly of Ghengis where not just given comands. The had to move up the ladder to some extent. His grandsons did not just sit on there asses and got comands, there was a a lot of competition.

Genghis skill as a general was truly great, but I think his biggest talent was picking out generals and leaders. He promoted what could be called slaves, people from outside of his tribe, even former enemys and so on. If you look at his closes generals, almost non where from his tribe. So I dont belive field armys under Genghis where so much better then when they were lead by Subadei or Jebe, however the armys Subadei and Jebe lead where build by Genghis out of literally nothing, there was a time when Genghis had to eat rats. This is why I consider him the greates leader and conquerer of all time.