Can I cast a spell after the stack has resolved on my opponent's turn in MTG?

Question

In a game, my opponent played Burn the Accursed to kill one of my creatures also deal 2 damage to me. I also have a 1/1 Scavenger Folk in play and the ability to create enough mana to cast Simulacrum, an instant which states

You gain life equal to the damage dealt to you this turn. Simulacrum deals damage to target creature you control equal to the damage dealt to you this turn.

The goal would be to take the two damage from me and place it upon the Scavenger Folk I control.

If I play this card in response to Burn the Accursed, the Simulacrum would go on top of the stack and then when the stack resolves in Last In First oOut order this seemingly wouldn't do anything as if Simulacrum is on the top because no damage has been dealt to me yet. Would I be able to let the stack resolve and THEN play my Simulacrum to move the damage to my creature, or is Simulacrum really only effective for damage dealt by creatures?

Answer 1

Rule 117. Timing and Priority covers who can cast spells and when. 117.1a allows you to cast an instant spell any time you have priority, and 117.3d means you will receive priority on your opponents turn any time they could take an action, but do not.

When Simulacrum resolves you gain life equal to all damage done to you that turn, which (as you've surmised) won't regain you the 2 life from lost from Burn the Accursed if played in response to Burn the Accursed.

However, if you survive the 2 damage done by Burn the Accursed, you will gain priority before the turn moves onto the next step/phase and can cast Simulacrum to gain back the life you lost.

Generally the optimum time to play a card like Simulacrum is during the end step, as long as you will survive to that point.

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Rules

117. Timing and Priority
117.1a A player may cast an instant spell any time he or she has priority. A player may cast a noninstant spell during his or her main phase any time he or she has priority and the stack is empty
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117.3d If a player has priority and chooses not to take any actions, that player passes. If any mana is in that player’s mana pool, they announce what mana is there. Then the next player in turn order receives priority.

Answer 2

I'll try to provide an intuitive understanding for when you can cast in MTG. There is a concept called priority, which is like a ball that players pass to each other. The player with priority is the only one allowed to do things. The priority ball by default sits with the player whose turn it is, but must be passed to the other players before anything on the stack resolves and before game steps advance.

If it is my turn, I can play any number of spells I want, and you can't respond. I have priority. Say I put five things on the stack. I want them to start resolving. So I pass priority to you. If you also pass priority without doing anything, the topmost thing on the stack resolves, and I get priority again. The stack has four things on it now. We can repeat this four more times - each time, I pass, you pass, and one thing instantly resolves. At the end of the chain, the stack is empty, and I have priority. If the last spell to resolve is a planeswalker, you can't kill it, because you don't have priority. I can activate its loyalty ability, pass priority, and then you can respond with a kill spell - but the loyalty ability is already on the stack.

Can I cast a spell after the stack has resolved on my opponent's turn in MTG?

No, because after the stack has resolved, the player whose turn it is has priority. Your first chance to cast a spell will be when that player passes priority. For example, if they try to go to combat, they are passing priority - you can now play your Simulacrum, or pass and let the game go to the beginning of combat step. If you do play the Simulacrum, priority immediately goes back to the player whose turn it is, and they can play more things, or pass (which again lets you play a spell, or pass to resolve the topmost thing on the stack, likely the Simulacrum).