1) Does the dagger's proficiency bonus count towards the melee attack?
No. No more than sword proficiency would help for a Swordmage's non-weapon attacks (ie: implement). You get the implement bonus, tho. Keep in mind these are attacks not against AC, so you don't need the proficiency bonus to make up for the gap.
2) Does dual implement caster's bonus apply to the melee attack?
um, do you have two implements? I don't see why not. You're delivering it as a melee attack, so it's more like an issue of range. Granted, I'm playing a sorcerer so I'm hoping I can have a second implement work for my melee build!
3) If using Acid Orb, which counts as a ranged basic attack, does that mean when used with a dagger it counts as a melee basic attack?
There's another feat that lets you do exactly that (I think it's reaper's touch, or something) so I'd guess not. Otherwise, what's the point of that feat? ...good question!
Build: I'm going wildmage for now, eventually MC Rogue/Daggermaster. I recommend human, for the bonus at-will, but Drow or Halfling aren't bad options either; in fact, drow racials are handy, and halflings have the re-roll thing. My Genasi will have a lot of resistances, but might not stack.
Another option is a Dragonborn Dragon Sorcerer, using the Dragonborn racial PP where you can fly. If you're going melee anyway, you can do worse than a high Str mod (athletics), plus a breath weapon; Con is a good thrid stat, I suppose, which plays off breath weapon damage. You're basically a tiny dragon at that point. Get Intimidate, and you've kinda got Dragonfear, right?
Still, wildmage and storm-mage-whatever, having Dex as the second stat, can go Con, Dex, Cha and have their defenses covered, plus a good AC stat.
Arcane Spellfury is great with AoE at-will (flame burst or something) and follow up with the Lightning at-will to shift into melee and hit, then move action out of melee. The Radiant AoE at-will is good, too.
There are some guide books in the WOTC charOp boards; while I don't agree on every suggestion (D&D is complex and situational, so putting all your eggs into one build-basket with not regard for that is still crazy).