Yes.

The first person is the speaker (me, I etc).

The second person is the audience (you).

Anyone else mentioned is the third person.

Yes:

• The first person is the speaker (I, me). It can also be extended to a group including the speaker (we, us)
• The second person is the audience (you).
• Anyone else mentioned is the third person.

Occasionally, perhaps as literary device or for comic effect, the first person may refer to themselves or the audience 'in the third person'. For example:

-My best friend is an idiot.
-I thought I was your best friend?
-Exactly.