i have a 質問 related to spells.Please read the details and answer.

Yea, there are things that go on in the seventh book that all seem to happen pretty fast - but I think the idea is that they all prepare for these things when they are at both Grimmauld place and shell cottage. Hermione (having prepared far もっと見る than the other two for their journey) probably learned the protective enchantments and then taught and practiced it with Harry and Ron. I imagine the case is the same with the Imperius curse since they determined they would need it at Gringotts.
Also, one of the things that is 発言しました about the unforgivable curses is that あなた have to mean it. Presumably, they learned how to perform the curses and later on they surely meant it when the situation was life または death at Gringotts.

Hope this helps! :]

They were shown the curse in 4th year, remember ? によって Barty Crouch Jr impersonating Alastor Moody.

Besides, it's the intention that fuels the magic. あなた may learn a spell but if あなた don't have the intention, it'll be weak - hence what Barty 発言しました which あなた quoted in your question. あなた have to mean it to make it efficient.

Therefore, they may imitate Hermione, it'll work as long as they have a real intention behind it. Remember too that Hermione had taught them many things, that Harry must have learnt many things to be able to teach the DA in OotP. There were many things left asides in both 本 and movies, we can imagine that they spent a lot of time together practising, especially Harry that had been keenly aware of the importance of defensive and offensive spells since Voldemort had returned.