"I am talking to you!"
Two questions here: "hozzád" is not accepted, is that an error? Second, is this the normal usage? As in: would "tehozzád" in this sense be preferred over, say, "veled" or "neked'?
"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.
Perhaps a bit like "He was talking at me" (but ignoring my replies or reactions) rather than "He was talking to me" (and listening to my response)?
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").