Yes, you can choose. Because the creature's ETB and the Vigil trigger are trying to go onto the stack at the same time and you control both of them, you decide the order to put them onto the stack. Whichever one is on top will end up resolving first.

Glad to help.

Yes, you can do that. Targets for a triggered ability are chosen when it's put onto the stack, but after an ability triggers it waits to be put onto the stack until the next time a player receives priority. In your example, Vigil triggers during the resolution of Marchesa's delayed trigger but the next time a player gets priority is after Marchesa's trigger is completely finished resolving, so the returned creature is on the battlefield when it's time to choose a target for the Vigil trigger.

The copy will also deal damage, so it's a total of 4 to your opponents. Rule 707.10 in the section of the rules about copy effects includes the following: "If an effect of the copy refers to objects used to pay its costs, it uses the objects used to pay the costs of the original spell or ability." This means the copy of Grab the Prize will be able to use information about the card discarded to pay the cost of the original to determine its effects.

Where you'll run into a problem is if there are cards with replacement effects involved that send send the card back to the library instead of the graveyard (they are still considered to have been "milled" in such a case). If your opponent has two or more copies of something like Progenitus, or if they have Wheel of Sun and Moon, then the game will draw.

Yes, you have the right idea. Activated abilities can be activated any time the player has priority to take an action, unless they're specifically written to have some restriction ("as a sorcery", "during combat" etc.). However, the legality of a block is only determined once, at the time the block is declared. That means giving an attacking creature flying after blockers have already been declared won't "undo" a block if the blocking creature doesn't have flying.

Yes, both of those work. Opalescence's ability affects all non-aura enchantments on the battlefield from the moment they enter to the moment they leave. Also, "dies" triggers and other leaves-the-battlefield triggers use information from the last moment something was on the battlefield to determine if and how they trigger. Preston, the Vanisher's ability will see a creature entering and Luminous Broodmoth's ability will see a creature dying.

A very interesting aspect to me is that Foundations feels like it's coming back around to how the original game designers probably understood the idea of a "core set". Collectible card games didn't exist in the way we know now and the team would have been very familiar with board games, RPGs and in-the-box card games. Even back then, there were plenty of examples of those kinds of games with a base set as the essential standalone version plus one or more expansions/supplements/add-ons that you could go out and buy to add new and interesting features to gameplay. With Foundations intended to be in-print and legal for 5 years, I feel like its role is much more comparable to that of base Settlers, base D&D, base CAH/Fluxx/etc. in terms of its relationship to the expansions around it. It can take care of most of the basic, stable, staple cards needed for the Standard format while the expansions give more nuance to the tournament environment and play around in the surrounding design space.

OyeGevoltageSurge: Answers to your question have been up for a while. Since there don't seem to be any follow-ups or corrections that need to be made, I marked one of them as the "Accepted answer" so this topic can move out of the list of unanswered questions. In the future you can take care of this yourself using the "Mark as Answer" button on the response that you feel is the most helpful answer to your question.

SteelSentry has the correct answer. The effect that allows you to cast the spell later is created by the resolution of Neyali's triggered ability. It's not tied to a static ability of Neyali, so Neyali doesn't have to remain on the battlefield for the effect to continue existing.

@legendofa: What you're reading is how the rules are meant to be understood and how they're meant to work, but they've unintentionally been written in a way that doesn't say what they mean. 509.1 (with its subparts) doesn't describe "the entire declare blockers step", it's specifically about the special action of declaring blockers at the beginning of the declare blockers step, and the rules seem to say this is the only time "blocked"/"unblocked" is determined for attacking creatures.

To be clear: I'm not arguing with your interpretation of what the rules are supposed to mean and I agree you're absolutely correct about what the result of this situation is supposed to be. This is a copy-editing problem rather than a weird rules quirk, and because I like thinking about the rules so much, it's just interesting to notice and consider it, especially when the rest of the document is written so tightly.

@legendofa: In the rules-as-written, the "blocked/unblocked" label gets applied in 509.1h, as the next to last step in the process of declaring blockers defined by 509.1, and it's not mentioned again for any of the other rules that describe the rest of the Declare Blockers step. The problem is that the things described in 509.1-509.4 happen in a specific order and Zareth San, the Trickster is entering the battlefield sometime after 509.4, so it technically wasn't around when attackers were designated as "blocked" or "unblocked", which would also mean for the rules-as-written in the Combat Damage step that it wouldn't deal combat damage. That is so unintuitive that it can't possibly be the intended result, because no one would ever play it out correctly.

I agree, this appears to be an oversight where the obvious and intended result (that Zareth is "unblocked" and will eventually deal combat damage) doesn't seem to be supported by the specific letter of the rules. A clarifying rule probably needs to be inserted between 509.4 and 509.5 to cover the hole.