Do rap/hip-hop musician sample jazz parts?
If you can sample jazz for hip-hop, then you should be able to live perform it in hip-hop too. You should be able to play some jazz piano patterns and have it fit.
I'm kinda old so I think of groups like Us3 and Jazzmatazz, but I know current musician also use jazz samples now. I just cannot name any names. Maybe try The Roots.
I think hard bop and modal are the jazz styles frequently sampled. Try listening to hip-hop with jazz samples and check out pianists like Bill Evans, Horace Silver, and Herbie Hancock. You will want to sort through the huge catalog of songs they recorded and look for the ones that emphasize funk and groove. Silver and Hancock will have more of that rather than Evans.
Starting point example: Us3 Cantaloop sampled Herbie Hancock's piano from Cantaloupe Island
I read your addition about karaoke...
... in karaoke there is often a backing melody...but for rapping part they put one note repeating
I still don't really know what this question is about. Are you trying to make karaoke backing track for rap music?
But, I'll just get back to your question as asked...
Why can't we play rap on piano?
I'm going to try restating that in a way that I hope captures your intent. "Why can't an acoustic piano mimic the sound of rapping without the words?"
In that case the issue is piano has fixed pitches for the keys but the voice has flexible pitch.
When talking our voices produce pitches and those pitches slide up and down freely. Even in some rap styles where the rapper maintains a sort of droning pitch, different parts of the lyrics can have shifts in pitch for emphasis. Such shifts many involve sliding, very small intervals, or even a dropping off of a distinct pitch in a very flexible way. A piano simply cannot do all that subtle, flexible shifting of pitch.
If you try to play the rhythm of the rap on piano (without the words of course), the problem will be the unchanging pitch of the piano. Even if you try playing a step up or down from a central note on the piano, the pitches will be very distinct and not at all like the flexible pitch of the voice. The result surely will be a very monotonous sound from the piano.
If not [piano], which instruments can rap be played on?
I think any number of percussion instruments would be much better suited for mimicking the rap. A snare drum with brushes can get a lot of subtle tones. A talking drum could also work, because they are pitched and importantly they have strings on the drum side that can be squeezed to bend the pitch.