Guanxi & other things I don't understand

During training they were always telling us about "guanxi", the guiding factor in Chinese culture. It basically means relationships and it's pretty hard to explain. One of the most interesting things is that I guess sociologists have figured out that, in the West, rules or laws kind of trump everything- so that if you break the law, you will be put in jail, and that's pretty normal, and any time you weren't punished that would be an anomaly. But here relationships trump everything- so that if you break a law but have a good relationship with the police, you'll be fine. Also there are lots of laws that are kind of meant to be broken- for example, they said that the building codes for Hess schools involve a certain number of toilets per kid (say 10 toilets all together) but the water code only allows for enough water to supply 8. So it comes down to your guanxi with the building inspector people.
In a way I guess it's like a network of trust & helpfulness. For example they said that if one foreigner goes to a scooter shop, and is nice to the owner, and brings his friends there to get their scooters fixed, then everyone gets better guanxi. This doesn't sound too different from how things go in the US- usually you will help people who need your help, and they will help you if you need it- but here it's much more pervasive and kind of more formalized. For instance, I was out in service and we stopped at a tea stand, and I said I'd treat and the sister said, "No, I will, I want to build up guanxi." And then what I truly wanted was green tea with 50% sugar, but that's the cheapest thing on the menu so she wound up buying me bubble tea, because it's more expensive, even though I can barely drink the stuff.
The thing I don't understand is whether guanxi is just a kind of building up of general good-will, or if I'm accumulating massive guanxi debts to a lot of people. Like in the US, if there was someone who needed a lot of help and didn't have anything they could do to help me, that would be OK, I would be happy to help them if I liked them and they appreciated it. But it's possible that here people have little guanxi calculators in their heads. That is extra-hard because I just can't do things like go buy tea for someone or go up to the counter in the restaurant to pay for meals because I don't know how. And should I if I could, or would people be mad at me for depleting their guanxi account? I have no idea.
The guiding principle is pretty much, live my life and smile and try to be polite. It's impossible to tell, at work for example, if all the Chinese teachers think I'm an idiot and can barely tolerate me, or if they think I'm average, or the greatest thing going. I guess this is true at many jobs but it's especially true here. So what can ya do. I just do as well as I can in my classes, and I try to build up some guanxi by being like, "Do you have any advice for teaching this page?" or "What do you think the kids will have trouble with?" But that doesn't seem to do it for them. No guanxi for me! :)