Spotlight only working from the finder

I don't know the definitive answer, but we could usually solve these issues by rebuilding the spotlight index. Takes a couple of hours, but most issues are fixed that way:

sudo mdutil -E / #deletes the spotlight index
sudo mdutil -i on / # starts the reindexing process

Additionally, you can use the commands here for an even more lowlevel approach

Regarding Observation 1:

As far as I understand, this is a long-standing bug in the way Spotlight is constructed (going back to Lion or even earlier). In Sierra it has just been acerbated to the point, where I have completely abandoned Spotlight and am using the Find (CMD+F) function in Finder. With this function I find all the files I am expecting to find and have also a larger array of options to choose.

According to my understanding the issue arises as Spotlight searches by strings and has some odd rules for defining strings, which appear to not be consistent at all.

Regarding Observation 2 and 3:

If a Spotlight search has been started the CMD-F function only returns the same as the Spotlight search. I can't figure out why it does do so. So you need to shut down the Spotlight search first to get a result with Find that is different from the Spotlight search result. It looks like the search results are not refreshed in between the two searches.

Further Observation to the issue of not refreshing search results: You search a file with Spotlight. Upon locating it you move it to a different folder. You use undo. From now on the file is found by Spotlight in the original folder even if it is moved again. But don't delete it - it is not a copy - it actually has been moved, Spotlight just refuses to acknowledge this.