First of all I come from a culture that is very low-power-distance. I would say that Mongolia is relatively higher, though perhaps not as high as other countries in Asia. Linguistically, this is partly expressed by a division in second person pronoun usage. There are two forms of the 2nd singular, ta used for older people, and chi used for younger people. All my students always address me as ta, except for a humorous lapse the other day, even students that are 10 years or more older than I, whom I feel should be address as ta by me. But this is just the tip of the iceberg. I am always addressed as "Teacher". Indeed, I am quite sure a few of my students have never used my name. But language is only one facet.
Students here basically ensure that I am taken care of. Perhaps some of this is also because I am a foreigner, but I am not any foreigner, I am their foreign teacher. So sometimes even things I think that I should do, or could do, they will insist on doing.
One of the first thoughts one can have is, "Gee, this is very nice!" Especially when the role of teachers can be so utterly disrespected in one's home culture, to come to a culture where on is indeed honoured simply for being a teacher is 'really swell'. I think it is fine to acknowledge this to some extent, provided it doesn't become self-indulgence. It genuinely is nice to work in a culture where teachers are respected.
However there are many things I feel like I should do. In fact, it can be embarrassing to have someone else do them. It can feel degrading to have others take care of something, degrading of them. This rubs against my egalitarian grain quite deeply. The inclination can be to confront some of this directly, but I have concluded this is not the best modus operandi.
When you confront some of this behaviour you are not saying, "Hey, we are equals here, please let me value you", or at least that is not the message being heard. More often what is heard on the other side is, "I don't value your culture and its ways, because it's wrong and you need to let me do these things my way." You actually devalue their whole culture, and devalue their attempts to honour you. This does not result in honouring them, but dishonouring them.
Of course, some practices can actually be burdensome for my students in unhelpful ways. The power distance gap results in unfair demands when really I am the one with superior means. In my view the best way to deal with this kind of situation is to circumvent it. For example, if students miss out on lunch because preference is given to teachers, the solution is not to insist students go first, but rather to avoid the situation in the first place. If I'm not there I don't need to be honoured in this way. (Actually this is not the only reason I avoid lunches! But "is foreign" works well enough as a reason. There is a loss in not eating together, but it's a loss I weighed and considered worthy).
Another issue arises from the combination of this power distance coupled with pervasive educational models of teacher-centered dictation learning. It is very hard to get my students away from, "What does the teacher think? Let's write that down. That will be the right answer." I am not always successful in dealing with this. In the west I might be flattered if someone thought my opinion counted. Here I am much more wary of giving straightforward answers. When students ask questions looking for a direct "Answer from Teacher Above", I work hard to ask my own questions, solicit student views, point them to grounds for arguments, etc.. This is not just a power-distance issue, but it does relate to it.
Finally, the teacher-student dynamic is so strong that having once taught a student, we are forever Teacher-Student. Former students will still call me "Teacher". There is no transition out of this relationship so far as I can tell. It's not like how, again in the West, a former student will sometimes have a new kind of relationship with their former teacher. Here we do not really transition. Again, this has positive and negative aspects. One can become very close to students, but always it is as their teacher. Or to say it another way, one may gain other aspects, of friendship, brotherhood, etc., but the teacher aspect will not be removed.