You get 11 halfling and 11 food, because X=11. It doesn't matter that you only paid 8 total mana, it matters what X is. You determine X when you start casting the spell, later on you add any additional costs (such as commander tax), then any cost reduction (such as Hamza's), then any minimum costs (which is just Trinisphere).

If you were casting Dyadrine, Synthesis Amalgam it would enter with 8 counters after declaring X=11, because it cares about the amount of mana spent rather than the value chosen for X.

When Horobi dies you have the option to put it in the command zone or leave it in the graveyard for Koh's trigger. If you leave it in the graveyard Koh's trigger will exile it and you again have the option to put it in the command zone. If it's still in exile when you activate Koh's ability, you can choose it, but at that point it will be too late to put it back into the command zone so it will be left permanently exiled.

The Gitrog, Ravenous Ride's ability must fully resolve before any other triggered abilities are put on the stack. You'll have to wait until after you've put lands out before you can search with Kura, the Boundless Sky. If the ability said "When you do" instead of "If you do" it would create a reflexive trigger that would give you the opportunity to slip the Kura trigger in between, but as written that is not the case.

Before the command zone was introduced, commanders were exiled rather than in an independent zone, that meant that if a commander was exiled by Oblivion Ring it could be cast from under the ring, but if it wasn't and the ring was removed, the commander would return as per the triggered ability. This was changed in 2011 and now if you move your commander to the command zone it becomes a new object that cannot be seen by Oblivion Ring. Similarly, if you use the state-based action to put Horobi, Death's Wail into the command zone, Koh, the Face Stealer will not be able to chose it with it's activated ability. Additionally, because it is a state-based action, you will not have the opportunity to activate the ability before it moves.

It would only fizzle the target if it were no longer a creature when it came under your control. Since Alexi's Cloak doesn't specify a controller (such as by saying enchant creature you control) it's target is still valid.

The answer to 2 is no. As originally printed, Lion's Eye DiamondGC says "play this ability as a mana source," which would allow you to move your spell to the stack, then activate it to pay for the spell. When it was printed you had to float your mana before announcing the spell, so it wouldn't have let you pay for a spell cast from your hand. To maintain the original functionality, Lion's Eye DiamondGC now says "activate only as an instant," which means you can only activate it when you have priority, not during the casting of a spell.

(10/4/2004) The ability is a mana ability, so it is activated and resolves as a mana ability, but it can only be activated at times when you can cast an instant. Yes, this is a bit weird.

This answer is almost correct, but the offspring aren't both able to see eachother. Offspring will trigger twice, so the first trigger will resolve creating a token, triggering the original twice. Once both of these new triggers resolve the other offspring trigger will resolve, triggering the original and the first kid twice each. The end result is 6 damage, as the first kid saw the second, but the second kid did not see the first. This is different from Immortal Servitude because in that case both creatures would enter at the same time, but with two offspring triggers they'll resolve on at a time.