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I think a point you may be getting confused by is that Nightmare Shepherd 's May clause is a cost, and costs for activated abilities and spells are paid as they're put onto the stack (so Night Soil would exile the cards before anything else could be put on the stack), but with triggered abilities the costs are paid on resolution, which means another ability like Tegrid, God of Fright's can make that cost unpayable.

To be more clear, state based actions handle the most common methods of losing the game: having 0 or less life, or drawing from an empty library. They also handle losing to poison counters. Winning or losing to an effect happens immediately, this could actually result in a situation similar to the one you're imagining:

If you have 0 cards in your library and 15 artifact cards in your graveyard when your Mirrodin Besieged (having chosen Phyrexian) triggers, you'll draw from an empty library before the targeted player loses, but you'll actually lose after them, possibly winning the game if they were your last opponent.

Some more points of clarification, because you do control it even while it's attached to a creature your opponent controls, if you have an effect that counts your artifacts (like Welding Sparks ) it sees the equipment.

If you're asking whether you get it back immediately to trigger it's ETB and equip it for free, it never leaves the battlefield, so it never comes back and triggers, you'll need to pay to equip it.

For some equipment, they have abilities that care about the controller of the equipment, not the controller of the creature. This is for simplicity since those should be the same person, but it can create interesting situations with a stolen creature. For instance, if you're Armix, Filigree Thrasher was equipped with Sword of Body and Mind instead, when it hit's you you'll mill 10 (as you were the one who was hit) and create a 2/2 green wolf token (as you control the sword). If it was equipped with Argentum Armor , you'd destroy target permanent when it attacks, you could even destroy Armix to keep it from hitting you!

Yes. Multikicker is a varient of kicker:

702.32c Multikicker is a variant of the kicker ability. "Multikicker [cost]" means "You may pay an additional [cost] any number of times as you cast this spell." A multikicker cost is a kicker cost.

Casting a kicked Everflowing Chalice will trigger Verazol, the Split Current .

Yes and no. All tokens have names. If a spell, like Llanowar Mentor tells you the name, it will have the assigned name. If it does not, it's name will be it's subtypes:

111.4 A spell or ability that creates a token sets both its name and its subtype(s). If the spell or ability doesn't specify the name of the token, its name is the same as its subtype(s). A "Goblin Scout creature token," for example, is named "Goblin Scout" and has the creature subtypes Goblin and Scout. Once a token is on the battlefield, changing its name doesn’t change its subtype, and vice versa.

However, when you're directed to choose a card name, you are limited to cards that actually exist. This means you cannot choose Elf, as that is Elf is not a card:

201.3. If an effect instructs a player to choose a card name, the player must choose the name of a card in the Oracle card reference. (See rule 108.1.) A player may not choose the name of a token unless it's also the name of a card.

Interestingly, you are allowed to choose Illusion and then have a token generated by Summoner's Bane tap for mana, because the token does happen to share a name with half of a split card.

@aznb01777 In the future, if you have any questions that need to be addressed, please submit them as new questions so they can be put into the new questions section for visibility. All the rulings I'll be listing will come from Prismatic Geoscope 's Gatherer page, and the rule from the comprehensive rules as of February 2nd 2021.

As was stated in this thread earlier, there are 5 basic land types as defined by rule 305.6:

305.6. The basic land types are Plains, Island, Swamp, Mountain, and Forest. If an object uses the words "basic land type," it’s referring to one of these subtypes. An object with the land card type and a basic land type has the intrinsic ability "{T}: Add [mana symbol]," even if the text box doesn't actually contain that text or the object has no text box. For Plains, [mana symbol] is {W}; for Islands, {U}; for Swamps, {B}; for Mountains, {R}; and for Forests, {G}. See rule 107.4a. See also rule 605, "Mana Abilities."

Having multiple basic lands of the same basic land type does not increase the mana produced by Prismatic Geoscope :

11/8/2016 How many lands you control of a particular basic land type is irrelevant to a domain ability, as long as that number is greater than zero. As far as domain is concerned, ten Forests are the same as one Forest.

Even though Snow-Covered Plains and Plains have different names, they share the Plains subtype, so they're not counted separately:

11/8/2016 To determine the number of basic land types among lands you control, look for the Plains, Island, Swamp, Mountain, and Forest subtypes among the lands you control. Count each subtype that appears one or more times toward the number of basic land types among lands you control. This number can't exceed five.

Note that the ruling specifically calls out that the number can't exceed 5. If snow-covered basics and regular basics were counted separately, it could go up to 10.

Another note, if you wait until after blockers are declared, blocking creatures that are removed from combat don't cause the attacking creature to become unblocked, that is, if Cowl Prowler attacks and you block with Hypersonic Dragon then cast Scrambleverse , which unfortunately ends up just giving away your Hypersonic Dragon and letting them keep the now untapped Cowl Prowler , it will still be blocked and deal no damage.