Hello Kostya,
thanks a lot for your help. What I should have mentioned right from the start: My mothertongue is German, which makes things more complicated, I guess.
But first of all: With the Swift-keyboard spell checking workes perfecly. Most suprising: After trying the Swift-k/b, my Samsung-k/b all of a sudden did the job, too - I had tried it several times before, but it definitely did not work this way then - very strange...
But still spell checking does not work with my Hacker's Keyboard (but it does with Android 4.2!) which is aparently the only one that supports typing German perfeclly, because it shows the layout of a normal German PC-keyboard, having separate keys for the 'umlaute' and most of all a feature that I haven't seen yet with any other k/b: It can be set to a mode that long-pressing shows the respective capital letter in the pop-up - since German orthography demands all nouns to start with a capital letter, we permanently needc capital letters, so this feature speeds up typing a lot.
Today I tried every k/b that might apply: Spell checking worked with some (not all) of them, but none of them is as convenient and flexibel as Hacker's Keyboard, which even comes with own dictionaries, so it's clear that it is meant to support spell checking... But since I cannot find a solution, I will simply have to decide: Spell-checking or convenience...
Anyway: Thanks again very much for your support.
Regards,
Tetta