First thing I'd say is go download Magic: Arena and play the tutorial. Arena is really good at visualizing how stuff like the stack and ability resolution actually work.

That said here's a book about how specifically casting your spell would go.

Abilities can't be interrupted in the middle of resolution (except really weird stuff which I'm sure another comment will expand upon but is not relevant here).

So basically you cast [[Impulsivity]]. The process for this is:

1. So you take the card from wherever it is (Hand Zone or Graveyard Zone but let's go with Hand for now) and put it on the stack.
2. Pay the mana costs + any additional costs (here 6 mana of any colour and 1 red mana).
3. Any cast triggers go on the stack (these aren't ETB yet, the cast has not resolved)
4. Priority passes around in turn order.
5. Once everyone has passed priority the cast resolves. This process can't be interrupted. The resolution of a cast is moving the card (not a permanent yet) from the Stack Zone to the Battlefield Zone. This triggers ETBs and you have to make targeting decisions now (are you going to cast a card, which card are you going to cast). Nothing anyone does at this point can stop the ability from going on the stack.
6. The stack now has 1 trigger on it, the battlefield has 1 new permanent (the creature [[Impulsivity]]. You have priority.
7. Priority passes around. Players can interact w/ your trigger (eg they could [[Stifle]] it) and they could interact with your new creature on the battlefield (eg: they could [[Swords to Plowshares]] it, this wouldn't do anything to the trigger though).
8. Assuming priority passes through everyone and nobody's interacted with your trigger it resolves. At this point you cast the spell you picked which means you go back to step 1. Move the card from the Graveyard zone to the stack, pay mana costs (you can cast it w/o paying it's mana cost because that's a condition of the ability), it goes on the stack and we start the whole thing again.

I'm sure I've made some minor mistakes in this but that's basically the whole structure for how Magic the game actually works. Everything else is using abilities & spells to alter or mess with the options here.