Interesting - it looks like nobody can take immediate or opportunity actions during the surprise round, either. Even if they aren't surprised.
Correct. In fact, it's explicitly stated that if you can not act in the surprise round, you can not take
any action. Furthermore, since you only get one action, you can't use any immediate actions on the actions you've used.
It also puts certain limits on some powers in the surprise round. For example, a Paladin can't use Divine Challenge, since "You can use divine challenge once per turn."
It would be pointless if you get turns in the surprise round, since you have to engage the enemy by the end of your turn. If you assume the surprise round is a turn, then you lose your challenge when your turn in the surprise round ends, since you can't take another action to engage.
Since the surprise round is not a turn, that line does not apply. The purpose of that line is to set a limit for how many times you can use it per turn. It doesn't apply to the surprise round, since it's not a turn.
I would allow it even if that turns out not to be the case, under the clause of "not screwing the players." Besides, I think it's a cool visual for the Paladin to burst into a room in surprise and throw down.
- It doesn't say that the surprised ones don't get turns, but simply don't get actions on their turns - look at page 277 on the page of conditions - compare stunned, unconscious and surprised - they use identical language (well, except the bit about free actions in the surprised condition, which is wrong).
At no point does the book ever use the term "turn" with the surprise round. The book even specifically separates the two in the description of combat. Just because similar language is used does not mean they are the same. For one, you can't have the "surprised" status any time other than the surprise round, which already makes it different.
- The rules specifically describe it as a "round", not simply as extra actions, and the rules make clear that in a round a creature ALWAYS takes the beginning and end of their turns (see pp. 268-69).
Those sections do not apply. Page 266 clearly delineates between normal rounds in which you get turns, and all the baggage that comes with them, and the surprise round in which you get a single action.
That said, I'm not at your gaming table, so I don't care how you play it. However you rule it, I think its important to be consistent.
I know you have rules ninjas poised to strike me down.

I agree, it's important to be consistent, however the DM chooses to rule it.
No turn = no beginning of turn = no ongoing damage in the surprise round. The party may be disappointed to find that that acid arrow that the wizard cast doesn't do ongoing damage to that nice clump of foes the wizard targetted.
That's correct.
Acid Arrow will do damage and apply the effect. Since ongoing damage happens at the start of the turn, you'll still get the damage against all of the enemies you hit. But you don't get to double-dip.
As well, it won't always be the monsters who are being surprised - while a party may be disappointed when their sleep doesn't work like they expected, I think they would be equally pissed by being surprised and stunned with no way to do anything for 2+ rounds.
Been there, done that - DM ambushed us while we slept, guard failed Perception check, I went bloodied from four hits before I could even act (and was still prone). It sucks, but that's why surprise is such a good tactical strategy.
One thing that is important to realise, that the save system of 4e with the condition being imposed on the attacker's turn and ended (by a successful save) on the defenders can result in a number of situations that "feel wierd" - one of which is the surprise round described by the OP. The "feel wierd" moment was likely hightened by surprise rounds being rather anemic in 4e - one typically can't even use a melee power in them, as one has to charge as their sole action.
That doesn't feel weird to me at all. That seems like exactly what would happen in a tactical situation. Your Rogues/Rangers/Assassins should be investing in Stealth to get in close. If you don't, you hang back and charge in at the right moment.
Another example of a feel wierd situation generated by the save/condition rules is if you hold an action and attack a monster on its turn - if you impose an effect on it (such as ongoing damage with, say, acid arrow), since it gets a save at the end of its turn, it may very well save before it suffers any ill-effects.
That's an unfortunate consequence with any sort of immediate reaction/interrupt, not with the save/condition rules.
Now, if one of those "feel wierd" situations surprises the players, I can understand how they might be upset. If they are aware of the way the mechanic causes "feel wierd" moments, it becomes a matter of tactics - rather than using sleep in the surprise round/holding an action with acid arrow, you use some other power instead.
Your examples don't entirely make sense to me. You'll still get the ongoing damage from
Acid Arrow, since they won't be able to save against it until it takes effect once. You'll still get the slow effect from
Sleep, and you still get the chance to fall unconscious. You don't get penalized for using them in the surprise round. You just don't get to double dip.