Highly ironically, you are describing the Buffy & Angel version, except that in that one, they do not breathe.:-) The idea of it, as I understand it, is that vampires were once a type of demon species - demon itself btw basically means "non-human" as in non-human sentient creature - but then when "something happened" (a goddess, or God, or some creature later worshipped as such, or perhaps entirely obscured by time), the original vampires were no longer "allowed" to remain in the human world. However, the Prime Evil did not like that thought, so converted the vampires to put on human flesh in order to hide them from the whatever it is that would not allowed a "true vampire" to exist.
Thus, modern vampires are converted from pre-existing ones by a vampire allowing someone to drink their blood, often biting them in return, which kills the human. As or perhaps after the death occurs, the body becomes "prepared" as a vessel that can hold the soul of a something else from an external, non-physical dimension. Fairly soon then, a vampire soul comes in to take possession of it, keeping it until it dies. Vampires enjoy having a body to ride around in:-). So note that here it is not all "freshly dead" bodies, only those properly prepared.
However, being (originally) non-physical creatures, they are not like humans. As you say, they would take on the personality of their host, although also they seem to be able to pick and choose among the traits - somewhat like humans also do, e.g. a coward could decide to become brave, or a smoker to quit, even though it may take some effort to change. The point though is that vampires wear their human body - or rather, their body that was heavily modified to support vampirism - like a puppet, and the personality is even included as part of that. They also have access to the memories of the deceased host. So they can look and act convincingly like not only a generic human but the exact one that they "possessed", but they are not bound by any of those convictions, e.g. fully able to take glee in their former lover's brutal mutilations and torture, even at their own hands, without a glimmer of a thought otherwise from the (now-dead) human that their bodies used to belong to.
Also they have a "second face" whereby their visage converts from normal human-looking to a more neanderthal-ish brow and the fangs come out, and their eyes turn yellow - essentially they "look demonic" in that form. This may affect their personality as well - the role they play in "blending in" to look like humans, vs. when the fangs come out and they just go for it. I believe it does not really affect them in most ways though - e.g. they are just as strong without it as with - and other than having fangs that are a ready source to tear open blood vessels with (though a fingernail or tool would suffice just as well?), they don't really "need" to do it at all. Though they do seem to enjoy it, more for the pain & suffering that their altered, uncanny-valley-like appearance causes to their victims than anything else.
But, they don't "need" to breathe - perhaps the conversion of the body to support vampirism burns out the medulla oblongata, or maybe they could (and do!) even, like you say just for the fun of it, manage a convincing simulacrum. But they are also EXTREMELY strong, and quite fast, so really all they need to do is convince someone for a fraction of a second before they get close enough to feed... or perhaps to convince someone to invite them inside their homes. Also, ironically they don't even "need" blood - e.g. they could totally survive for years, even millennia, trapped somewhere where they are cut off from access to air, water, contact with others, and yes blood. They just enjoy it is all.;-)
So in this lore, I think the main horror for the vampire to be trapped in a coffin at the bottom of the ocean would be the excruciating boredom, not so much any physical sensation of wanting to breathe but not being able to. Also, many of them literally enjoy the pain sensation:-) - after all the body can't really die all that easily, and unlike humans who also have souls but were born inside their bodies so never really knew of any other existence, vampires, having once been elsewhere, are very aware that they definitely do not need to "fear" death, or at least in the same way that a human might. So the signals can be interpreted differently. Some vampires are better at this than others though - some are more animalistic and controlled more by their immediate urges, while others can rise above them, postponing their tortures in order to wreak even moar havoc and mayhem later.
Okay, that's a lot of text - I hope you find at least some of it interesting:-).