When you take dagger expertise, etc. it doesn't seem to say that you need to use the dagger as a weapon for the bonus to apply, only that you need to attack with it. Is casting a spell through a dagger considered attacking with it? If I plan to use my dagger as a melee/ranged weapon, do I need two sets of feats for it?
I assume no (to requiring two feats), but I need to do some reading on Implement Expertise.
Same issue with magic items like the frost dagger, and it's even more ambiguous here. Does using a flaming dagger make my acid orb into a fire-acid orb?
This was actually addressed in a FAQ and not as an errata that clarified the rules, which is disappointing. In this case, your spell would only gain the Fire keyword and fire damage when you cast the spell through the item's daily power by using it as a free action to add 1d6 fire damage.
Melee attacks might seem like a special case, but they aren't as far as I know. Spells cast through an item don't use that item's physical damage dice, so they do not gain the benefit of an item's at-will power that changes the damage type of its physical damage dice.
Same issue with rogue sneak attack. I channel my spell through my dagger, so I am making an attack with my dagger, so technically I should be able to use sneak attack with this attack. This goes for rogues who multiclass as sorcerers as well as sorcerers who multiclass rogue. I guess it's potentially an issue for half-elves, especially if they use that feat that gives them an extra at-will. A half-elf rogue that can sneak attack with fire spray all the time would be pretty funny.
That seems fine with me. Rogues have always been able to multiclass as Rangers to gain extra dice once per combat, and Dragonborn Rogues could sneak attack with their breath weapons if they won initiative.
Same issue with daggermaster paragon path. Does this path make dagger-channeled spells crit on 18-20?
I'm inclinded to say no, but I need to read the paragon path to see specifically what it does. Attacks made with a weapon ≠ attacks channeled through a weapon as an implement.
Same issues as above when the sorcerer uses the dagger to make melee spell attacks via a certain feat.
The answers are the same because it still doesn't use the weapon's damage dice.

Another issue with that feat: when a spell that counts as a ranged basic attack is channeled into a melee attack, is it considered a melee basic attack, a ranged basic attack, or neither?
I need to reread the feat, but I believe it would be treated as a Melee Basic Attack.
Does this change when you look at opportunity attacks?
Given that Opportunity Attacks must be Melee Basic Attacks, I would say that the above applies.
What about those bracers of mighty striking-type items?
I assume that this is a bug in the
Character Builder, and that you would need the melee version of those bracers or lose the bonus to damage. I need to read more on this as well.
Note that allowing all of these things to work dagger implements wouldn't overpower sorcerers. They already do less damage than rogues and rangers in exchange for having a better selection of area-affecting encounter powers. Their at-wills do a little bit better damage than a wizard's, with almost no control features added in. In most battles, we've seen that half of our attacks end up being at-wills, so a little boost wouldn't hurt all that much.
To be honest, I answered these questions before reading all of your post, but I think my responses are reasonable.

A side issue on implements: if you use a two-handed weapon as an implement but never as a weapon, do you need to hold it in two hands to do so? Can you off-hand a staff implement and then not be allowed to use it as a quarterstaff without clearing your other hand?
I assume so. Presuambly Weapon Properties apply only to attacking with a weapon and not to using it as an implement.