1. to fixate, to fasten (Not common in that sense, but you can find it for a hand brake for example.)
2. to determine, to assess, to observe, to notice (Coming to a realization about reality after some observation. Sounds a bit more technical than "merken" and "bemerken")
In English you could kind of use “to observe” for someone basically just stating something. It sounds fairly fancy and is not the main sense of the word. I think you could say “she made the observation that most people tend to prefer summer to winter”. “observation” in this context would be about the act of speaking rather than either the moment of realisation or literally looking at people. I guess it’s similar to the verb “to remark”. Does feststellen have this sense of observe?
Yeah, that works. Managers often say something like “Ich stelle fest, das hier alle am Handy sind.” and that’s definitely a mix between noticing and remarking.
cool dankeschön!