When applying for exchange at US university, only using ESTA (visa waiver program for Europeans (EU)), I may only "observe research" but not "conduct research". What does "observing research" include? I could not find any examples.
This sort of visa waiver has restrictions because it is not a visa that allows you to work. "Conducting research" is work. "Observing" research or learning how to research isn't work, it's learning/education. Generally, laws that limit activities granted to foreign visitors are intended to protect labor: both to prevent jobs from being occupied by foreign visitors over citizens, to prevent exploitation of visitors who lack other protections, and to make sure the government gets paid the appropriate taxes.
There are likely to be differences in the exact letter of the law (which is also certainly vague) and how it's dealt with in practice. Really this is not something we should address here, it's a legal advice question where even slightly wrong answers from people you don't know on the internet could put you at legal risk. The distinction between work and non-work is not as clear in some fields as others, and the people writing these restrictions don't have every possible case in mind.
If you're in a restaurant, the difference between cooking a meal and observing someone cook a meal seems like it should be fairly plain. An observer could ask questions, could watch the preparation, but couldn't add an ingredient, stir a pot, flip a pancake, plate a meal. However there's a bit of gray area on what sort of feedback they could provide: "this could use some salt" doesn't really seem to cross a boundary in that situation, it's the type of feedback any visitor might give. However, if you're at a food manufacturer and deciding how much salt to add is normally a job given to a food science professional, that sort of input could be seen as "work".
The institution you are visiting should be able to help you with this, though, and you shouldn't need to hire your own lawyer. You're likely not going to be the first student to participate in this exchange, so you could ask about what sorts of things previous students have done.