The short answer is no, there are no standard phrases that must be used in order for the verbalization of your action to be binding. (this may not be inclusive of all poker venues).
Whenever you make an action in turn it is your burden to make that action in a clear unambiguous manner.
There are is you describe some "cute players", but for the most part, players making unclear comments, are fishing for tells. This in itself is not particularly against the rules, may or may not be good play and may or may not be considered good etiquette.
The answer using your first examples is yes this guy has made in all in bet, assuming he is head up with the guy, if other players are behind his actual bet is the amount the player he is referencing has in his stacks. It is clear to player B what player a meant so that is going to be taken as player A's declaration.
In your second example the dealer may have been in error on a couple of levels. First is that the player did not agree with the dealer so the dealer made a decision that should of been a floor persons decision. The details you gave were not enough for me to speculate about what the correct decision would be, but in a general way I think the dealers decision was likely incorrect.
When I make decisions as a floor person there is information I need. What might surprise most people, is that what the person thought they were saying is totally null data for the decision. Because what the person knew or claimed they were saying was indeed something that was vague and would not be clear to the other player. The primary question I ask is "what do you think he meant? I will also listen to a few other players describe what they heard. If what was said can reasonably mean what was heard, what was heard is going to be what player A is bound to. (As an aside this also applies to hand motions that might cause a player to check).
A few favorites are players in a game were a six dollar bet can be made, say "sex" which can sound like check or six.
In a noisy poker room, a player said quietly said to the player on his left whom had just bet large, "are you" then much louder added "all-in". I asked my question what did you hear, Player B heard all in, the Dealer heard all in , a couple players said all they heard was all in. Player A swears he said "if you were all in", and I believed him, but I ruled against him because he was making a move. The move was simple, trying to be vague so anything he said really did not count. Players really, you say something and something is going to count.
Others are how some players instead of saying did you check? Say "check?" with the question emphasis. It is common for a player to hear check, and really do I have to figure out in a noisy poker room if you mean check or not when you are being vague. Same goes with all-in.
I have never had a problem making rulings like this. Because player A can never deny that the root of the incident at the table was because they were vague, and it seems they are ready to own their vagueness, even if they don't like it. And while my experience is that most of the time these people are being sleazy and taking a shot, I know it, the other players know it, that particular fact really does not need to have context in the decision, thus these decisions go very smoothly.
I would like to add a note, this particular decision making process may not have precedence were you play.