Chiedilo a lei

Ask it to her: This is not correct. You can say something to someone, but you can't ask something to someone.

Ask her: This is another commonly used expression though again it's more of an idiom than correct grammar. It is a shortened form of "ask her about it".

Ask it her: Again, you can't ask something someone.

The most common expression would most likely be "ask her about it".

Please read my previous comment first.

Don't tell it to me. This would work if you are telling someone not to tell you which card they have picked. This would be the closest to normal English. However magicians and other stage performers still probably wouldn't say that if they asked you to pick a card; they would say "Don't tell me what the card is" or "Don't tell me which one it is". It would be less common, but not wrong, to use "it" as the pronoun in this case.

Don't tell it me. This is incorrect. You need to tell qualcosa TO qualcuno.

Don't say me. This is also incorrect. You can never say qualcuno, but you can say TO qualcuno.

Don't say it to me. This is grammatically correct but would not be used in your example. When you give someone information (such as the name of the card that they've chosen, you normally tell them the information.

Don't say it me. This is incorrect. You can only say something TO someone.

Unfortunately these are both expressions that you can't translate parola per parola.

In italiano si usa la stessa parola per entrambe "say" e "tell", ma in inglese.... there is a subtle difference.

"Saying" is something that you can do yourself. You can say something when you are alone in the middle of a desert. Because "saying" does not require a listener, you never "say me qualcosa". (Though you can "say qualcosa TO me".)

However "Telling" requires an object; someone or something that is being told. Also it usually involves giving the listener information. In this case, it is correct to say "You told me qualcosa".

"I said that the card was the three of diamonds" means that you said those words. There does not need to have been anyone around.

"I told you that the card was the three of diamonds" means that you said those words to me.

So looking at  your examples:

Don't tell me. This is an acceptable and common abbreviation of "Don't tell me the card". "Don't tell me" by itself is an idiom meaning either "I don't want to know" ("Don't tell me. The gearbox blew up again.") or "I already know" ("Don't tell me; the bus is 15 minutes late again.") However it only works if the listener is clear about what it is that they aren't supposed to tell you.

Ogni terzo tentativo è grammaticalmente sbagliato, buoni i primi due in ciascuna, ad eccezione di "Don't say me". Puoi dire, "Don't tell me which [one]/[card] it is".

In generale "Ask her" Chiedi a lei 

                    "Ask it to her" Chiedilo/a a lei