"Please look up difficult kanji in your dictionary."
"Hiku" is a Japanese word that happens to have a lot of idiomatic uses. It basically means something like the English verb "pull" or "draw" but it often seems simply to fill the role of verb in expressions such as "jisho wo hiku" or "piano wo hiku" where the action has, at least to the English speaking mind, litte to do with pulling. In such cases the idiom just has to be remembered and the appropriate translation has to be what describes the action required with the object of "hiku" as in "consult a dictionary" or "play a piano." This is more of a vocabulary problem than a grammar problem. It is similar to the problem of learning all the uses of "to fix" in English.
When I looked up the verb 引く（ひく）, it doesn't really mean "look up (something)." It may be more helpful to think of it as "to use (something)". If you think of it this way, the sentence means, Please use the dictionary for difficult kanji. And that means "the dictionary" is the direct object.
What confuses me, is why some of the sentences use the を participle and others use で for the dictionary.
In this case, the meaning of "ひく" is seaches for the meaning of the difficult kanji OR make sure the difficult kanji with dictionaries.
The "で" has been used for making sure it with something in this case. For example, "じしょ"で"ひく", this means to check about something it and then make sure it, and then "じしょ"を"ひく", this means to use dictionaries. BUT for example if you listen, "くるま"で"いく", this means to go somewhere by car. The meaning of "で" is changed like this.
Even though I am an native Japanese, it is difficult to understand it.
The particle "wa" marks the topic rather than the subject of the sentence. It says that the predication (the verbal structure to follow) applies to what it marks. Often the topic is the "subject" of the verb but it does not have to be. Here it is not. ("(What I'm talking about is) difficult kanji (and what I'm saying is) look them up in the dictionary.)
You've made a couple of mistakes here.
You can't use the particle に with 辞書（じしょ）here: you're saying that you're using the dictionary to look up the kanji, so you need で instead. に can never be used to indicate that something is being used as a means for something else, で must always be used for this.
Also, your verb choice is a little off, it's not completely wrong, but it's not quite right either. 見る（みる）means that you're seeing the kanji, but doesn't really carry the implication that you're searching for specific kanji.
There's a number of sentences that you could use for this, here's a couple that I verified as being correct with my Japanese teacher:
学生達は辞書で難しい漢字を引きます。（がくせいたち は じしょ で むずかしい かんじ を ひきます）
学生達は辞書を引いて難しい漢字を調べます。（がくせいたち は じしょ を ひいて むずかしい かんじ を しらべます。）
The verb 調べる（しらべる） means "to look up" or "to search for", and is used when searching text.
It is flexible but the direct object phrase almost always appears to the direct left of the verb. And the verb will almost always be at the end of a phrase. You can explore alternative word orders if you wish but native speakers are going to think you odd and foreign speakers might not understand what you're trying to say.
じしょをひく is a set phrase meaning "consult the dictionary." (ひく also means "pull" or "play an instrument," so maybe you're pulling the dictionary off the shelf?) If you're going to break up the phrase, I suppose you could use で to indicate the means by which you're doing something.
From what I understand, あなた is used only when you don't actually know the person's name. It's super formal and actually kind of rude in some situations. Generally, you'd either leave it out and let context do the work, or you'd actually say the person's name. The exception would be a wife talking to her husband, in which case あなた is kind of a pet name.
In my opinion, if you need to follow the order of the words, you should answer "辞書で難しい漢字を引いてください", something like this. However if I were you, I will answer on this way, "難しい漢字は辞書で調べてください". It is more natural Japanese. The meaning of "引いてください" is the same with "調べてください".
Your answer, "辞書は難しい漢字を引いてください" this means, for me, the dictionary has a soul and it is living and it has its own mind, and then the dictionary start to look up the difficult kanjis by itself. It looks something weird.
“辞書は“ without another particle (e.g. では or には）marks 辞書 as the topic but seems to mean that it is the agent or recipient of the action of the verb, which is nonsensical. The dictionary is neither the subject nor the object of the verb. Its "oblique" relationship to the action should be marked specifically. Your sentence would mean something like "(As for) the dictionary, please look up difficult kanji." You need to express the "in" or "with" to make a possible sentence.