These Prediction spells cannot take themselves into account
These spells tell you information about what would have happened if you didn't cast the spell.
Say you plan to go down a road, and ask Augury about it. It tells you Woe. You decide to go down it anyway, but really stealthily. This time the assassins waiting for you don't get the drop on you, you kill them, and take their fancy stuff. You have changed the outcome to Weal. Augury couldn't take your actions resulting from its own casting (like casting Pass without Trace, or grabbing a couple of guards to come with you) into account.
It's obvious why it can't take itself into account - if it had the answer would have been Weal, but because it told you that the answer would have been Woe, etc.
So that's what the caveat means from a narrative standpoint - that the very casting of the spell may change the predicted outcome.
The GM cannot take the players, or the dice (completely) into account
Say the players ask the GM via Augury about a plan to attack a powerful monster. The GM thinks "Hmm, based on how they've described this plan, their general combat tactics, and their current strength, they should be able to take it down". They answer "Weal".
Then the players deviate from their plan massively, and one ends up dying. Or the dice just really don't go their way, and one ends up dying. Oops, I guess the answer should have been "Woe"/"Weal-and-Woe", instead. But since the GM is not omniscient, it wasn't.
In this case, the caveat is a get-out-of-jail-free card for the GM - they answered the prediction spell in good faith and to the best of their ability, but they still won't always be right.
No, there is no way to know that Portent was "used"
Portent is an unusual feature in that it leverages the distinction between the player and their character. Obviously, it is the player's choice when to replace a roll with a foretelling roll, but within the fiction, this does not correspond to any action or even any thought or intent on the character's part. All the character does is witness the fact that the glimpse of the future they received earlier that day has indeed come to pass.
To put it another way, when a foretelling roll is used, nothing changes in the present. Instead, the player retroactively decides what vision of the future their character has already received in the past. Hence, there is no detectable effect to be noticed in the present to determine that the feature was used.
This interpretation is supported by the first sentence of the feature, which is the only part that describes how it works rather than the mechanics of using it:
Starting at 2nd level when you choose this school, glimpses of the future begin to press in on your awareness.
Also note that no action or reaction of any kind is required to use the feature. If Portent represented an active manipulation of probability or fate by the diviner, it would make more sense for it to require a reaction to do so. Contrast this with the Wild Magic sorceror's Bend Luck ability, which explicitly does actively manipulate fate, and requires the sorceror's reaction to do so (emphasis added):
Starting at 6th level, you have the ability to twist fate using your wild magic. When another creature you can see makes an attack roll, an ability check, or a saving throw, you can use your reaction and spend 2 sorcery points to roll 1d4 and apply the number rolled as a bonus or penalty (your choice) to the creature’s roll. [...]
In the case of the Bend Luck ability, the sorceror is using their force of will to change something rather than passively witnessing something they had seen in a vision. In this case, it might not be unreasonable for the DM to rule that the victim sensed some kind of probabilistic funny business going on, e.g. "I'm sure that rock I tripped over wasn't there a second ago!"
Immunity to frightening (or another condition) is not a dead giveaway for your secret magic item
To address your specific problem, immunity to fear is not a terribly rare effect, so that alone isn't necessarily going to tip off your players that a special magic item is in play. Furthermore, if your players do infer that a magic item is protecting NPC from fear, they will most likely assume that the item does that and nothing more. From your question, it seems like the item in question probably does a good deal more than simply protect from fear. But if you're really worried about your players figuring it out, I think the best advice is to make sure you can still tell an interesting story if they do so, even if it's different from the story you had planned.
It seems that the fear effect was just an example, but the same can be said of most other condition immunities. At worst, your players will probably suspect a magic item or spell that specifically protects from that one condition.
Best Answer
Identify will reveal the nature of the magic
The Identify spell will "Whether any spells are affecting the item and what they are". This will at least identify the Evocation spell affecting the envelope.
Clairvoyance will let you see in the envelope.
Clairvoyance will let you put a sensor inside of the envelope. You will likely have to manipulate the envelope from the outside to make room for the sensor, however (which might pose some risk or difficulty); the GM will have to make a call on how much room is needed
Since the inside of the envelope is dark, you will need a way to overcome that; Darkvision is a possible option (although a bright enough light will probably work well enough.