"I am talking to you!"
"Hozzád" and "tehozzád" both should be accepted. "TEhozzád" basically emphasizes the built in pronoun, so it is a more stressed version.
On the choice of words... Hungarian is somewhat different here from English.
"I am talking to you" in English is a normal way of saying that we are talking, having a discussion.
In Hungarian, when "(én) hozzád beszélek", it specifically means that I am talking and you are listening. The above sentence could be said by a principal to a mischievous student.
To talk, to have a conversation or a discussion, is expressed with "veled". With you.
And "neked beszélek" is interesting. It is similar to "hozzád beszélek", but it has this connotation that you are ignoring what I am saying.
Yes, something like that. It is not easy to explain. But the first examples that are coming to my mind are negative ones:
"Ne beszélj itt nekem hülyeségeket" - Don't give me all this BS.
"Beszélhet neked az ember....!" - Meaning something along the lines of "Whatever I say to you has no effect on you". ("Beszélhet" means "... can/may talk/speak").