There are two ways to interpret that sentence, and it hinges on a weirdness of how English uses the indefinite article.
Any character or monster that doesn’t notice a threat is surprised at the start of the counter.
The usual interpretation of "a threat" here is that it means "one threat". If that is the correct reading, your question is the result. Is it correct though? This meaning would require that surprise is a relationship between two individuals, so that the dire wolf could be surprised by the rogue but also not surprised by the enchanter.
Is this how surprise works? It turns out, no:
If you're surprised, you can't move or take an action on your first turn of the combat, and you can't take a reaction until that turn ends. (PBRv0.2, p. 69)
Surprise is not a relationship between two entities, it is a state of a single entity. It's impossible to be surprised by one opponent but not surprised by another.
Is there another way to read that sentence about "a threat" that makes surprise sensible as a state? As it turns out, yes.
"English is funny that way"
Another use for the indefinite article, which looks identical to the "one threat" meaning, makes the sentence in question
Any character or monster that doesn’t notice a threat is surprised at the start of the counter.
mean any threat at all, not just one. If this meaning of "a threat" is how it's being used, then that means only creatures who notice no threat are surprised.
Because this reading is perfectly normal English, but ambiguous, we need to confirm the reason by looking for clues in the surrounding text. That confirmation is in the definition of surprise we looked at above: being surprised means being completely surprised, which only makes sense if it happens when no threat is noticed.
So the dire wolf is not surprised, because it did notice a threat, as opposed to not noticing a threat. (See how that makes sense put that way?)
On the plus side, the champion and the rogue don't need surprise to have advantage on the dire wolf, because that doesn't rely on surprise, but rather on being unseen, and being unseen is a directional relationship, not a state.
The rules don't provide strict limitations to distance, DC or any other conditions to succeed the check. They are supposed to be described in the adventure itself, or set by the DM.
There are suggested checks in the LMoP which specify distance explicitly:
Spotting a secret door from a distance of no more than 10 feet without actively searching for it requires a passive Wisdom (Perception) score of 15 or higher
But in this case it's up to the DM to set the distance. It is reasonable to make the check before the attack, to justify surprise.
Best Answer
Surprise and stealth seemed to be explained in better detail in the Starter Kit
The Lost Mine of Phandelver features a small goblin ambush (as seen in the WOTC Livestream). The rules walkthrough for the stealth check and the suprise round says to roll once for all the goblins (adding their +6 stealth skill) and compare that one, party-wide check to Passive Perception of the PCs. PCs whose passive is less than the goblin stealth check are surprised and do not act in the first round.
This concurs with the Basic rules where in general one part or the other has the possibility of surprise depending on who is trying to set up an ambush.
1 player/PC scouting ahead of the main party would be treated like a separate party for the purposes of surprise round. They might find some goblins, fail to be noticed by the goblins, slip away warn the party, then the party as a whole could try to stealth forward.
A player showing up late to a fight could be hidden if they make a suitable stealth roll (i.e. some kind of cover) giving them advantage.
If the monsters and the main bulk of the party have already spotted one another/are engaged in combat I don't think a player who is further behind would in anyway get a surprise round compared to everyone else, no matter how good their stealth check. The enemies have already been alerted to the presence of the party (their enemies) and will be wary as the combat commences.
However if that player is trying to sneak into the combat, they can and should get advantage if they make a good enough stealth check.