At the start of the skill challenge, if I don't tell the players that this is a skill challenge, they are likely to mostly propose role-played actions that are hard to translate into a skill check, e.g. shouting out "Hold the thief!"

The players can, but don't need to know which skill/ability to roll. Pure RP actions are just fine even if they don't match a skill. You tell them what they can roll when they describe what they're doing, or whether they need to roll at all. Shouting at a crowded marketplace doesn't take much skill, but is unlikely to stop a skilled thief either, so they'll have to follow up with something else. Eventually they figure out they'll need to do better and use their skills. Also, just announcing the beginning of a skill challenge isn't necessarily a bad idea either.

In response to a general "what do you do?" prompt, some players are more likely to answer than others. Should I impose rules that ensure that every player gets a turn in the skill challenge and participates?

If this is a problem in your particular group, limiting rolls per player somehow is appropriate. It doesn't have to be either "free rolls" or "turn by turn" - you can decide that the character who succeeded in the last roll is busy carrying out the successful action and can't help with the next roll.

Also don't forget to mix up challenges with different skills; having a Stealth/Thievery/Streetwise -heavy challenge can be done single-handedly by Ron the Rogue if no other rules are imposed.

How do I handle ideas which I like from players, but which don't really correspond to a skill? Like in the example above, shouting "Hold the thief!" sounds like a good idea to stop a thief from running away in a city. But it would translate badly into let's say a Diplomacy check, especially if the character isn't skilled in that.

If it translates badly, don't translate it. Not everything they do needs to be rolled. Just tell them the action is impossible, or doesn't achieve the desired effect. If the idea is particularly crafty and clever, you can give them a free success. If the idea is particularly bad (tickling the sleeping dragon) you can give them a free failure. It's always up to you.

What if somebody proposes a good idea which corresponds to a skill that isn't listed in the primary or secondary skills for that skill challenge?

Let them do it. The primary and secondary skills listed are just suggestions anyway.

what do I do if the players want to cast spells instead of using skills?

It's the GM's call. Some powers have little combat value and yet see use extensively in the RP segments (for example, the Wizard's Cantrip). You can choose to limit the powers your party can use, and it makes sense as it prevents everything from boiling down to combat, but if you do so make sure it's got a sensible reason, like the thief constantly disappearing from view where they're hard to target.

Once the initial spontaneous idea have gotten used up, how do I prevent the players from simply checking their character sheet for their best skills and just proposing those?

I don't consider this a huge problem myself. Skill challenges are supposed to be an opportunity for the players to use their best skills. As long as they describe what they're doing, let them go with it. The example in the guide isn't a misuse of the mechanic - for players who don't know the monster manuals and other guides inside-out it's often difficult to remember which knowledge skill (History, Arcana, Religion, Nature...) matches which topic.

Rules as written: the subtleties of "can see" you're reading into don't exist. Whether you "can see" something mechanically means "you have line of sight to it." This heavily implied by the Player's Handbook, and finally made explicit in the Rules Compendium's section of Line of Sight on p106:

A few powers do require a user to be able to see a creature to target it, however. For instance, a power might specify that it targets "one creature you can see." In other words, the creature must be within the user's line of sight.

So the Warlock's curse simply refers to those enemies to which you have line of sight. You have line of sight to someone simply if you can trace the corners of your square to the corners of their square, and that's it, so whether you're covering your eyes doesn't change anything. Since covering your eyes doesn't change your line of sight, the only RAW answer is: nice work, smart guy — you still have line of sight to all the other monsters.

The rules are built on the assumption your characters are generally trying to look around and be aware of their surroundings, and not pulling these tricks. If it doesn't make sense why you can't use a spyglass to affect who you can see and change your line of sight, it's because you've exited rules territory, and at that point the rules aren't expected to make sense.

The RAW way to eliminate line of sight is to manoeuvre around obstacles and eliminate it. So that's what a Warlock wants to do, if they want to get creative with limiting their Curse targets by vision.

How can this make sense or be explained in interpretation or story?

Before this, there's a big principle of D&D 4e to understand: it prioritises balance and fun mechanics above rules making total sense story-wise. Thus the mechanics do not bend or adjust to what makes sense simulation-wise: powers and features do what they say, and it's up to the story to make sense of that. There is no attempt to simulate things realistically, which is a major point of contrast to previous editions, and a contributor to D&D 4e dismantling the Omnipotent Wizardry Tier of classes.

So, given this 4e ethos, the axiom is that Warlocks can only curse the nearest enemy in line of sight (whether the Warlock's covering an eye or not). As BESW points out, this is a fun and interesting part of the Warlock's tactical decisions. It's up to the Warlock's player and their companions to make sense of why this is the case, which could be a pretty fun opportunity to flavour your Warlock or their magic.

• It may be the nature of the curse. It refuses to be cast any other way, or picks its own target.
• The Warlock may be capable of casting it another way, but have good reason not to. Doing so may lead to very, very bad juju. Doing so might be violating their pact.

How would I handle someone trying to do this?

How we'd handle it in our own games is a matter of opinion and style. Some would allow it (especially if they're a fan of rule-of-cool and it was cool). Others would ask the Warlock to put the telescope away. I'd probably do the latter, so as to not have the small headaches that might follow from wandering outside the rules into simulationist territory.

It is a fun feature for a Warlock to deal with (having played one myself), and truthfully, having read how BESW would approach this, I'd do as he does.