So choosing to not be as effective as possible when you have that knowledge is metagaming.
You have no knowledge of either how many death saves are needed, when they occur, or how many have been made or saved. Metagaming would be acting on that knowledge above that you don't have. Not metagaming would be healing the person ASAP so he doesn't die...............like you described.
But the wizard's not taking comprehend languages because he knows that's this bard's whole thing, and he doesn't want to step on that player's fun.
1) If that's the bard's whole thing, that's a pretty sad bard.

2) it doesn't step on the bard's toes, since comprehend languages is not bard specific.
But the game is more fun when they don't rest constantly, so they don't do the cautious safe thing as if they're actually concerned about their lives.
My point is that resting after a fight is usually just as unsafe. I mean, you just had a fight there with a monster and are probably in a dungeon or ruins. And if you leave and let the denizens know you were there by discovering the bodies, they will prepare for you and you have a fairly high chance to TPK when you return. Pushing on is often the safest thing.
No, obviously not. But the player who knows who Zhentarim are explicitly leaning into the fact that they will likely be betrayed because that's fun and interesting is.
Zhentarim are bad as an organization, not at the basic level. It's the leadership you need to worry about. Also, they are a country/city state, so they don't just betray every time they talk to someone. That's dumb and successful evil isn't stupid. You only betray when you can get away with it and it's going to be to your significant advantage. Talking to some adventuring shmoes is not usually going to be such an opportunity, so you won't usually be betrayed.
But choosing to do so because he's who the module is about when we agreed to play this one, is, even if you justify it in fiction after the fact.
No. You are still not bringing in out of character knowledge to act upon it. Let's say we all agree to play an evil campaign, but we agree ahead of time we will not betray one another so that the campaign won't fall apart. Creating evil characters that can have close ties and commitments that they won't break is not metagaming or even wrong. Evil can love. In fact, a lot of evil in the real world has stemmed from love. A father murdering someone to get medicine to heal his daughter, and so on.
The same goes with what you describe above.
Metagaming would be if you knew because you read the module that the patron would pay more than 10 gold, but not more than 50 or he would get upset and send you away, so you bargain hard to get to 50 and then abruptly stop because you the player know what will happen.
If you're portraying someone who is abjectly selfish and amoral, and tried to steal from the party, but retconned your actions the second the another player said they don't want to play that sort of game, it is.
Evil can be committed to the group and out to burn everyone else. It happens all the time in the real world. Evil can be loyal, especially in small groups.
As for what you describe above, that's moving the goal posts and not what you described in your initial post. The player and/or DM should have been up front during session 0 and just said, "No evil" or "No stealing from party members."