Deathspeaker

Yes. Only the casting cost is reduced to (0).

Yes! As long as you control the spellcaster, the game sees it as a spell 'you' cast, meaning the player.

Normally no, because Deathrite only triggers when the minion dies, and the Deathspeaker's ability banishes the minion. But, if you somehow kill the minion at the same time it enters the realm (e.g. Bottomless Pit), then Deathrite would trigger. The token dies because of Bottomless Pit (interrupting the Deathspeaker's ability), Deathrite resolves, then the token is like all tokens when it dies.

You cast the minion spell. Pay mana, meet threshold, banish it from the cemetery, identify where it will be summoned. The minion enters the the realm. (It is a copy of the banished minion.) 'Enter the realm' effects trigger and resolve. These include: Genesis abilities. Effects like , , , , etc. See '' in the for more details. The minion is banished. The intent is that the can speak to the dead, invoke their abilities, and then release them into the afterlife (whatever that may be). See also '' and the example with plus a 's genesis. The Deathspeaker's is analogous, since the minion will enter, splitting the Deathspeaker's ability on the , the genesis ability will resolve (along with any other triggered abilities based on a minion entering the ), then it will get banished.

Yes, because events on the storyline are split up when a card enters the realm. See the 'Splitting Events on the Storyline' codex entry for more details.

Yes. You control it when it enters the realm, and then it gets banished.