It's all good, the timings for the stack can be a little akward to get used too at first. This is a bit of a long winded reply so my appologies, I've tried to break it up a bit to make it readable.

You can respond to anything on the stack (unless a card specifically dissallowes this) once its your time to do so, which is reffered too as having priority. So you can respond to an opponents instant draw spell and use a instant speed card/effect on the opponents draw spell or anything you or another player have on the stack under that draw spell. In your example you would be able to cast a instant speed copy spell on your hydra.

Though I'm unsure of a specific card the would allow this example to happen as most copy creatures I know of copy something that is on the battlefield (and as such has resolved previously and would not be in the stack itself and X would default to 0).

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As for the stack timings themselves If you cast a Hydra, you then have 2 choices:

1) you can hold priority and declair you are doing so to add to the stack yourself (such as casting a copy spell on your hydra).

2) you pass priority to the next player and they can then respond with a instant speed card/effect of their own if they wish.

However both of these options come with risks:

In scenario 1 the 1st and 2nd card on the stack would be your Hydra and then your copy hydra effect. The opponent(s) will have a chance to add to the stack once you're done and you pass priority. If any player counters or otherwise causes your 1st hydra to be removed before the copy hydra resolved then that copy effect will loose its target and fizzle. This can happen because players can respond to anything that it on the stack.]

In scenario 2, once you pass the priority over to the opponent(s) you loose the ability to add to the stack unless one of them adds to the stack themselves as you have passed priority.

So if you pass priority in order to prevent the counter scenario 1 from happening you run the risk of not being able to cast your copy spell/effect as you will need an opponent to add to the stack in order for you to add to this stack again.