"Ask me anything" and "Ask anything to me"

There are some sentences I hear regularly:

1. Ask me anything
2. Ask anything to me.
3. If you ask me whether he was right, I would tell you "No".
4. If you ask me about whether he was right, ....
5. If you ask to me whether he was right, I would tell you "No".
6. If you ask to me about whether he was right, ...

So I hear the construction between ask + me + something but I like to know which sentences are correct above?

And also could you please explain the grammatical rule of these sentences?

And more quick thing, I told my native english speaker friend this "Do you know whether Eric asked me today". And his reply was "I don't know what Eric asked you about." However I meant to ask whether Eric ever looked for me or not. Was my question wrong?

All of your examples with to me are grammatically incorrect. The verb ask takes an indirect object and a direct object, and the indirect object cannot usually be moved to an oblique phrase with to. So the following are correct:

1. Ask me anything.
2. If you ask me whether he was right, I would tell you "No".
3. If you ask me about whether he was right, ....

And the following are incorrect:

1. Ask anything to me.
2. If you ask to me whether he was right, I would tell you "No".
3. If you ask to me about whether he was right, ...

The problem with your question Do you know whether Eric asked me today? is that you've placed me in the indirect object position. This makes for a bizarre question in which you ask your friend if Eric has asked you any questions... which makes no sense. What you meant to say was Do you know whether Eric asked about me today?

In modern English The direct object is the person you are asking, the indirect object is thing you are asking for - usually with "for".

So

I asked him for a light

is grammatical, but

*I asked to/from him a light

is not.

Contrast "I requested some help from him", where the thing requested is the direct object.

In older English, you find the construct "ask something of somebody", but that is literary or archaic now.

With many ditransitive verbs, you can put the indirect object before the direct, without a preposition, as

I gave him the book = I gave the book to him

but this construction is not normally available with "ask":

*I asked a light him

is not grammatical.