Yes, there is a system for that. All cards available to your class first has to have its base requirements satisfied. Then they could potentially show up, depending on how the other players did in their respective categories.
Each card is scored and their individual score is also multiplied by a weight. As you noted environmental kills for instance is considered "very cool" so every score is multiplied by some hidden factor. Match on fire is a card that has to be over a certain level to show up (base requirements satisfied), but whenever it does it has a big score multiplier and this basically means that it is more or less guaranteed to be showcased in the end. In comparison, I have seen eliminations show up with very low numbers, so this would mean that it has a low base condition.
It's only 1 card per player, so to get the healing card when you have 4 environmental kills would probably mean having up around 15k healing (this is not real numbers, I'm just trying to explain how it works) for it to be "your best card".
At the end if not enough people has a "personal best card" that reaches a base score then fewer cards are shown. This is why we sometimes see only 3 cards, or fewer. I have never seen 1 or 0 cards but theoretically it could happen.
This is all speculating by the way, nobody except Blizzard themselves knows exactly how it work. This is just some things we can infer from observing how the system behaves.
D.Va is unique in that she has two ultimates. They charge separately.
Self-destruct behaves like other ultimates. It is charged by dealing damage and over time, while in her mech . It persists through death.
Call mech is reset to 0 whenever D.Va's mech is destroyed. This means that if D.Va is killed while on foot, she will not retain Call Mech charge. It is charged in the usual way- damage and time while on foot- relatively quickly. It is instantly fully charged when her mech self-destructs or if she is resurrected by Mercy.
D.va's interface and voice lines will only display and reflect the relevant ultimate. Annoyingly, this means there is no way to see her self-destruct progress while on foot, or waiting to respawn.
Best Answer
It appears that when D.Va deletes a Moira's Biotic Orb with Defense Matrix, she gains ownership of it for a split moment. Any healing that the orb is doing at the time of it being deleted is credited to D.Va.
A similar, but rarer bug has been around for a long time and is known to affect Junkrat as well. I am not sure about the causes of that one, but it seems related to getting healed while calling a new MEKA.