I know that Zilean and Yorick can't use their ultimate abilities on a friendly Shaco's clone but can a Mordekaiser use his ultimate on it? Also can he get a ghost from my clone if he kills me and the clone but he doesn't use it on the real shaco?
Mordekaiser received a rework since the previous answer was posted, which completely changed the way his ultimate works. Previously, it applied a damage over time effect that would create a clone pet of the target for Mordekaiser to command if the target died under its effects, and this could target and affect Shaco's clone.
The ultimate's description now reads:
R - Realm of Death - Cast time: 0.75sec
Mordekaiser slows the target enemy champion by 75% during the cast time, after which they're banished together with Mordekaiser to the Death Realm for 7 seconds.
Units between realms see each other as spirits, considering each other dead and negating any interactions between the two. Only the target and Mordekaiser will enter the realm; other champions cannot follow them. Everything that occurs inside the Death Realm is hidden, and all still inside are killed at the end.
For the same duration, Mordekaiser also consumes the target's soul, reducing their current attack damage, ability power, total attack speed, maximum health, armor, magic resist, and size by 10%, in addition to gaining them for himself. If the target dies while inside, Mordekaiser keeps their partial stats until they respawn.
If one of the two affected champions leave the Death Realm, because of having died or having it dispelled, the other will do so as well, but the stats will remain stolen for the full duration.
Shaco's clone, while considered a "champion" for the purposes of most abilities, is not affected by Mordekaiser's ultimate ability now. Mordekaiser will perform the cast animation, but both he, and the clone, will not teleport to the Death Realm.
Here's a gif, taken from this video, highlighting what happens when this interaction occurs:
Not pictured is that this does put Mordekaiser's ultimate on cooldown, so it is not beneficial whatsoever for Mordekaiser to use his ultimate on a Shaco clone.