Basically, the answer to this question lies in the understanding of the phases of the turn.
there are a number of phases and steps that a turn goes through, here is a brief overview:
- Untap step
- Draw step
- First Main Phase
- Combat phase (has many sub steps, skipped for understanding)
- Second main phase
- End step
The above is not an exhaustive list, but it gives you enough understanding to get your head around what's going on.
Whoever's turn it is, that player is the Active Player. The other player(s) are Non-Active Players. This terminology will help with explaining things.
The best rule of thumb is "The active player has priority right now." 90% of the game this will be true. and during this time you can't do anything. To clarify a little, Whenever a new phase or step begins, the active player has priority. Think of it this way, the active player moves into their main phase, they have lands to play and spells (including creatures) to cast, and this is where that process all starts.
The next thing to understand is how the stack works. Again, a good rule of thumb is "if something happens, it usually uses the stack". For example, casting a creature uses the stack, activating Olivia Voldaren's ability uses the stack. Casting Oblivion Ring uses the stack, so does it's enter the battlefield trigger (there are numerous answers about these for further information) essentially, anything that doesn't directly generate mana uses the stack. I say directly, because Scalding Tarn's ability will get you mana after it resolves, but it does not generate mana and DOES use the stack.
Here is what happens with the stack:
- Someone puts something onto the stack
- That player gets priority and could cast additional spells if they wish.
- After that player passes priority, each subsequent player gets priority.
- After all players pass priority, the object on the stack resolves.
When a player has priority with something on the stack, they can cast instants (or spells with flash)
if someone chooses to cast something with something else on the stack, then the whole process repeats for THAT ITEM until it has resolved, and then steps 2-4 are repeated for the Original item.
let's look at an example:
Albert is in his main phase, he casts Ancestral Recall. Oh no! Nancy is wisely playing islands, and with Counterspell in hand, wants to tap 2 of them to make sure Albert's day is ruined.
Here is how this looks on the stack:
1. Albert casts Ancestral Recall. Ancestral Recall Goes onto the stack.
2. Albert wants to do nothing and implicitly (by sitting there doing nothing)
3. Nancy gains priority and responds with Counterspell.
4. Nancy gains priority and implicitly passes by doing nothing.
5. Albert gains priority and, looking smug, says "In response" and slaps his own
Counterspell onto the table. Poor Nancy!
Uh oh, things are getting complicated now! Here's a look at the stack
Albert's Ancestral Recall
6. Albert gains priority again, and again silently does nothing.
7. Nancy doesn't have anything else to do so she disappointedly says "Resolves."
8. Albert's counterspell resolves.
9. Nancy's counterspell is removed from the stack, so we skip back down to just
looking at Albert's Ancestral Recall.
10. Crossing his fingers, Albert passes priority.
11. Grumpily, Nancy says "Resolves." She has no more answers.
12. Albert's Ancestral Recall resolves. He cackles maniacally as he
draws 3 additional cards.
This demonstrates how things work with the stack. This passing of priority happens everywhere. If Albert wants to go to the combat phase, he passes priority and Nancy might do something in his main phase. If Albert wants to end his turn, Nancy gets an opportunity to cast some spells before her turn starts.
hopefully this has helped understand the stack, in answer to your bullet points:
- Instants can be cast at any point where you have priority, all required targets and no restrictions prevent you casting them (e.g. you can't cast Doom Blade with no creatures on the battlefield, and you can't cast anything after Silence resolves).
- Tap abilities can be used any time you can cast an instant, excepting abilities that state otherwise (such as Birthing Pod's). Remember that creature have "summoning sickness" (creatures that you haven't controlled since the beginning of your turn may not activate abilities with the Tap or Untap symbol unless they have haste).
- Instants and abilities are put onto the stack to resolve, and can only be placed there by the player who has priority. Hopefully the above has explained when this happens.
Most of the time, priority passing happens fluidly and implicitly. As a result, usually it is enough to know that "in response" means that the spell is still on the stack, and you get to do things if you want at the end of each part of the turn.
Here is an interesting situation with how the stacks and priority work to show how you can't do whatever you want, whenever you want.
- Alberta casts Lingering Souls, a powerhouse of a card against Norman's deck, and passes priority.
- Norman has a Surgical Extraction in hand and wants to use it to stop the spell being flashed back and clear the other copies away to limit the damage, but the spell is on the stack so he cant exile it yet, he passes priority and the spell resolves.
- Norman wants to cast Surgical Extraction, but since the spell resolved, priority reverts to Alberta. He has to wait until Alberta moves to a different phase or casts some other spell to get priority.
- Alberta gets greedy and fancies 2 more tokens, she flashes back Lingering Souls straight away. Poor Norman's Surgical Extraction is now a dead card. The Lingering Souls is on the stack and will then be exiled.
There are times where priority has a massive impact, and the above is one of them.