From a British English perspective.

Sentence a) is incorrect. Sentence b) is perfectly grammatical.
In response to a declarative sentence that the telephone is ringing I would reply:

I'll answer it.

To actually say, "I will go and answer it" is overly formal. The subject and the auxiliary is nearly always contracted in speech. Furthermore, to point out you will go and do an action is unnecessary but this type of construction is common in speech.

A: We don't have any more milk.
B: I will go out and purchase some milk ---> I'll (go and) get some

From a British English perspective.

Sentence a) is incorrect. Sentence b) is perfectly grammatical.
In response to a declarative sentence that the telephone is ringing I would reply:

I'll answer it.

To actually say, "I will go and answer it" is overly formal. The subject and the auxiliary is nearly always contracted in speech. Furthermore, to point out you will go and do an action is unnecessary but this type of construction is common in speech.

A: We don't have any more milk.
B: I will go out and purchase some milk ---> I'll (go and) get some.