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.
In combat, most creatures stay alert for signs of danger
all around, so if you come out of hiding and approach
a creature, it usually sees you. However, under certain
circumstances, the Dungeon Master might allow you to stay
hidden as you approach a creature that is distracted, allowing
you to gain advantage on an attack before you are seen.
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.
If you read the following paragraph in the PHB after the section you mentioned on turn order (pg. 189) you'll see it says:
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.
On top of that, it's important to note that
A round represents about 6 seconds in the game world. (PHB 189)
So in this case it translates to:
- Warrior takes his turn. He can choose to ready an action here to use his reaction later to attack Elf2 when the Rogue attacks Elf1. Note that the Warrior can move into range if necessary and will not affect surprise as surprise is determined before turns are taken.
- Elf2 does nothing and is no longer surprised. He can now take reactions. If the rogue attacks him there are no bonuses related to surprise added to that attack.
- Rogue takes his turn. When the Rogue attacks Elf1, the Warrior uses his readied action.
- Elf1 does nothing and is no longer surprised. He can now take reactions.
- Combat proceeds as normal using the same initiative order. (Readying an action does not change initiative order so it will still be Warrior, Elf2, Rogue, then Elf1)
Best Answer
You take your turn and can act as normal
The Weapon of Warning (DMG, p. 213) states:
You have stated that your companions were all outside of the range for this effect, however that does not prevent it from working on you. From the rules for Surprise we have:
It is important to note that surprised creatures still roll initiative and have turns in the initiative order, they simply cannot act on their first turn. Since you can't be surprised you are free to act as normal on your first turn. If you manage to roll higher initiative than your enemy you can indeed attack before them, this is exactly what this item was designed to do.