Is a player allowed to hold their cards across the "line" so as to suggest that they are going to fold in order to get a read on others at the table? Are they allowed to continue doing so hand after hand, or can the dealer call the hand dead?
This is a very good question. In a very technical sense a hand is not "folded" until it is released over the line. They key word being released. As long as a player is holding their cards or has them protected with chips on top of them it is not a dead or folded hand.
That's not to say you might not get a ruling otherwise, you might depending on where you play, and how much your opponent shenanigans are considered angling under the local rules and how fed up the dealer and the floor person are with the player etc.
However the only upside I see calling for a decision on something like this is that it might be a fun and effective counter needle for the player.
As you play more poker your are going to run into Donkeys like this all the time, doing all kinds of little angles. The particular angle you are asking about is a total fools angle. Some green players fall for it sure, but for more experienced players it is very telling stuff, as most amateur angles are. So learn what a player like this is telling you about his hand when he pulls the BS and take advantage of it to relieve him of his hard earned money rather then letting the player get under your skin with the stupid tricks. This player is telling you things, use the information and don't discourage their stupid moves.
So as a dealer, I've had this situation occur many many many times. To put it bluntly if it's angle shoot, as you said to try get a reaction out of a player, I'm informing the player not to do so and calling floor to get a round penalty once the hand is over. No questions asked.
Now I'm certain most dealers, and myself included, would give any player a chance. You can tell pretty quickly if a player is new to live casino poker, and in that case most dealers will be fair, inform the player they can't do that, explain why and give them another chance. I tended to give players 2 chances, on their 3rd time I punished.
The above is only for players who are clearly new. Most casinos, tournaments and cardrooms have what is called a forward motion rule, and it's to stop exactly what you're describing. When a player is knowingly doing this to get a reaction, in any place worth playing they're breaking the rules and angle shooting. The same applies for chips, i.e. moving chips forward and then moving them back. So will the hand be killed, no it shouldn't be, but the intent was clear as a fold, and then not to fold the intent is clearly an angle shoot. Which is cheating.
If your dealer doesn't call floor, don't forget you have the option as a player to call floor too if you want, so do so.
As for a dealer calling a hand currently in a players hand dead, not just to this situation, I believe only a floor has that power when they suspect cheating or foul play, so you know.
Different casinos may have different rules, generally the players are meant to have their cards behind the line.
Other players will normally not have a problem with a player that has their cards over the line as long as the cards are not being moved in a forward motion.
If a player is making a tough decision and he starts to push his cards forward while staring at his opponent without the intention of folding, then this is clearly against the rules (or an angle if there are no rules against it).
It is ultimately up to the dealer and the floor whether or not an action is legal in their poker room. If you come across this again, I would suggest that you call the floor over if the player is consistently pushing his/her cards forward without folding.