The usage of “Que” is quite simple and I think you already understood it.
“Ce” used before it is a pronoun used mainly to make a reference to something. Most of the time it’s either because what we are talking about is obvious, either because we don’t really know what the object is referring to.

For instance: “Donnez-moi le livre que vous tenez” could be “Donnez-moi ce que vous tenez”.
In this case, the speaker may probably be unsure about what the other person is holding.

“Vous avez beaucoup de livres, donnez-moi celui que vous avez en main”.
In this case, the pronoun is used to avoid repeating the word “livre” already used, but the speaker knows that the other person is holding a book.

However, you cannot use “Ce que” and the word it’s referring to at the same time. So “Le livre ce que vous tenez” is incorrect, either remove “Le livre” or “Ce”.

Note that in this case, we will mostly used another pronoun “Celui/Celle” (depending on the word gender). Again in your example, “Montrez-moi ce que vous utilisez” is not really correct because it implies you’re not sure about what the other is using. “Montrez-moi celui que vous utlisez” would be more approriate in this case.

About “Dont”, it is used to refer to another word used earlier in the sentence without having to repeat it, most of the time you will use it two bind two sentences talking about the same object.
For instance: “J’ai acheté le livre dont vous m’aviez parlé” allows you to mention two things about the book (the fact that you bought it and the fact that he talked about it) without having to say “Livre” twice.

• que is used to introduce a subordinate clause where what que refers to is a direct object. What it refers to is a word which is present in the main clause.

• ce que is used to introduce a subordinate clause where what que refers to is a direct object. What it refers to is not a word which is present in the main clause and its description holds completely in the subordinate clause. (It is analyzed as ce the demonstrative neutral pronoun and que; ce is a pronoun which never replace a word, it is just a place holder here, in other contexts it can replace something in the context or a preceeding clause).

• dont is used to introduce a subordinate clause where what dont refers to is a complement which would be introduced by de in other contexts. What it refers to is a word which is present in the main clause. If what it refers to complete description would holds completely in the subordinate clause, you would use ce dont (again the pronoun ce holds the function in the main clause, and dont holds the function in the subordinate clause).

Examples:

Donnez-moi le livre que vous avez vu.

Is the combination of “Donnez-moi le livre” and “vous avez vu le livre”.

Donnez-moi ce que vous avez vu.

Is the combination of “Donnez-moi ce” and “vous avez vu ce“. The only thing we know about ce is that you have seen it.

Donnez-moi le livre dont vous avez parlé.

Is the combination of “Donnez-moi le livre” and “vous avez parlé du livre”. (Additional difficulty: de le livre is not correct and de le is constracted in du)

Donnez-moi ce dont vous avez parlé.

Is the combination of “Donnez-moi ce” and “vous avez parlé de ce“. The only thing we know about ce is that you have spoken about it.