Now the Immortal Prelate dies. Several turns later I play Da Undatakah. If he picks up the Immortal Prelate's deathrattle, will he pick up all 4 deathrattles the prelate had at the time of death (and then deathrattles from 2 more minions), will he just pick the original one the unbuffed minion had (and then deathrattles from 2 more minions), or will he just pick 3 random deathrattles from the available pool?
I assume based on the wording that it's the first (but given the inconsistency in wording in the past and odd card interactions, that may not be the case).
Now, given the answer to the above, if the minion had no initial deathrattle at all, but you gave him an artificial one via one of the above buffs, can Undertakah pick it up now as one of deathrattle minions or would that not be the case because the minion didn't have an initial deathrattle and thus wouldn't be up for consideration as a deathrattle minion?