Note: If all that's needed are guidelines for determining the DCs of Dungeons & Dragons 3.5 static skill checks, the Player's Handbook (2003) provides general guidelines for static DCs on Table 4–3: Difficulty Class Examples (64) and the Dungeon Master's Guide (2003) has more examples on Table 2–5: Difficulty Class Examples (31).
Skill check DCs don't, by default, scale with the PCs' levels…
In a role-playing game system like Dungeons & Dragons, Third Edition and its ilk that tries to emulate reality—that is, in a largely simulationist system—unchanging skill check DCs are the norm. The difficulty of a task is established first and then folks try to perform that task. (Contrast this with determining who's performing the task first and then setting the difficulty based on that performer!)
To a degree, such a system empowers both the DM and the players: both know exactly what creatures can accomplish, and what they can accomplish serve as benchmarks that indicate their proficiency. For example, a level 1 PC has a Climb skill modifier of +3. The player can look up in the Player's Handbook the skill Climb and determine that, if the PC can take 10, then the PC can climb a knotted rope or cavort about in a ship's rigging, but the player must roll if the PC is wants to go up a tree.
Thus the player and the PC know that if that PC takes 10 to monkey around in the rigging and still fails that something untoward's afoot. For example, maybe circumstances (sinister circumstances) have made the rigging more dangerous, or maybe the PC's affected by something (a sinister something) that penalizes his skill? No matter. This failure—when success should've been certain—merits an explanation or, at least, an investigation.
This notion of knowing a PC's capabilities (and, perhaps, by extension possible outcomes of those capabilities) before an action is attempted—this reliability—is often absent in role-playing game systems that use exclusively scaling DCs.1 If the DC for a Climb skill check, for example, depends on the PC who's making the Climb skill check, then neither player, PC, nor DM actually knows how good a climber that PC is! There's no way to determine any creature's actual proficiency at a task with the universe always increasing a task's difficulty so that it's in line with the performer! Rather than some tasks becoming easier as the creature gains in proficiency, everything stays just as difficult.
To return to the example: If the PC arbitrarily can, even in the most generous of circumstances, always possibly fail to cavort about in the ship's rigging or shinny up a knotted rope, the player and the PC will be reluctant to attempt those tasks because disaster always looms. A chance to roll is a chance to fail.2
This, too, may seem realistic: in real life, there is always the chance of failure, after all, but life's random number generator is far bigger than the d20 this game uses! I mean, if even a master climber always fails 5% of the time when he tries to get up that knotted rope, for instance, that failure is at least embarrassing and at worst deadly. Imagine if you, dear reader, had a 5% chance of failing at everything you attempted, from making breakfast to tying your shoes to driving to work. Were the universe that horrifyingly random, I doubt many of us would make it through the day alive much less unscathed. (Also see this question.)
(To be fair, Dungeons & Dragons, Third Edition et al. do have some elements that scale to the PCs—the most important probably being an encounter's Encounter Level—, but these are specific exceptions rather than general cases.)
…Used sparingly, though, this isn't all bad!
You, however, aren't alone. Other folks do feel as you do: that some tasks should always carry with them a risk of failure and that element of risk should be in line with the potential proficiency of the creature attempting the task.
For example, Crafty Games's d20-inspired FantasyCraft (2009) has a section Using Sliding DCs (370). (Yes, it's a big book, but, to be fair, this is near the end.) That section sets the DC of a level 1 PC's Easy task to 10, Average to 13, Tricky to 16, Hard to 19, and Desperate to 22. For every 2 levels a PC gains those DCs pretty much increase by 1. As FantasyCraft has many of the same benchmarks as Dungeons & Dragons, Third Edition et al., these numbers might serve as a decent scaffold on which to build your for own similar house rules for Dungeons & Dragons, Third Edition.3
To be clear, accustomed as I am to Dungeons & Dragons, Third Edition et al., I've found FantasyCraft's idea of sliding DCs very difficult to conceptualize. That is, it's difficult as a GM and as a player to imagine that the universe thinks that no matter folks' experience levels they should always remain challenged by the same things.4 Nonetheless, I've also found the idea playable enough: sliding DCs are the exception, and there's sufficient reliability in the remainder of the system to be able to determine what folks are actually good at.
"How many skill checks should an adventure have?"
I think this may be two different questions.
How many skill checks should PCs have to make to experience all of an adventure's content? This depends mightily upon the adventure's depth and length. To be clear, though, as this fine answer explains, if success on a skill check is required for the adventure to progress, then either success on that skill check should be automatic or the players should be told that they'll have to adventure elsewhere until their PCs are higher level and return later to continue this adventure.
Beyond that, it's totally okay to gate some extended content behind certain skill checks. That rewards PCs who've invested in certain skills. For instance, if it takes an Appraise skill check (DC 30) or Knowledge (local) skill check (DC 25) to determine that the little 100-gp gem is actually worth 10,000 gp to the old wizard in Drawkcabnowt—and the PCs won't be shorted gp after the adventure if they don't realize this—, then that's totally okay. Likewise, if the PCs don't succeed on a Search skill check (DC 25) to discover the secret chamber, then they wont fight the ghouls, won't get the XP for that encounter, and won't acquire the ghouls' meager hoard. That, too, is usually okay… y'know, as long as the adventure isn't called, like, Where Are the Ghouls Hiding? or something.
In short, I recommend preparing necessary content first and then gating some interesting but unnecessary content behind skill checks… and, of course, behind other things, too, like character background, experiences in other adventures, rumors picked up in town, and so on.
How many skill checks does it take to yield a challenge that's worth XP? Based on Traps (Dungeon Master's Guide 67-76), it seems that if it's possible that, by failing one or two skill checks, the PCs will exhaust some of their resources, then making those skill checks can be considered an encounter. Based on the difficulty of the checks and the resources that'll have to be expended to deal with the consequences of failure, those skill checks can then be assigned a Challenge Rating (and an Encounter Level and subsequently XP). However, that's not the whole story.
XP is typically earned for encountering the trap, whether that means drunkenly blundering into it or adroitly disarming it after having discovered its cunning trigger. Either way, the XP's the same. What matters is that there's a risk of the PCs depleting some of their resources.
For instance, PCs that fall into a pit might have to climb out and, sure, those who don't will die, but the PCs already should've gotten XP for the pit. Similarly, if success or failure on a series of Climb skill checks to reach the mountaintop is worth XP to the fighter that does so, that shortchanges the druid who bypasses the Climb skill checks yet nonetheless expends resources to use wild shape to assume eagle form and fly up there.
To sum up, I recommend assigning a CR to a general problem (like The trap is CR 3) and not assigning a CR to a specific task or an absolute number of skill checks (like It's CR 3 to avoid the trap by succeeding on 1 Search skill check (DC 23) then succeeding on 1 Disable Device skill check (DC 25)). That makes it so the players can solve the problem without worrying that their PCs solved it wrongly because the players failed to read the DM's mind about how the DM thought the problem should have been solved! If you're going to make something worth XP, assign a CR to reaching the mountaintop rather than assigning a CR to climbing the mountain.
1 I've seen such systems sometimes disparaged as quantum bears. That is, a system in which the GM determines a task's outcome based solely on the result of the character attempting the task, ignoring the setting's role. For instance, a poor roll when exploring the cave may see the PC attacked by bears that wouldn't've been present had the player rolled better.
2 A chance to roll is a chance to fail was coined by a player in a near-decade-long GURPS, Third Edition fantasy campaign that I GMed. In that 3d6-roll-under system, an 18 is always an automatic disastrous failure. The coining player's PC routinely failed Ride (Horse) skill rolls despite a skill of 15 or less. On several occasions, the PC severely injured his limbs,… and the game mandates a Ride (Horse) skill roll every time a character climbs aboard a horse! Eventually, even when horses were available, the PC walked.
3 In the interest of full disclosure, I have a playtest credit for FantasyCraft, but don't worry: you buying it doesn't give me money.
4 As a fan of the video game series Borderlands, though, I get why this happens.