If I use my longsword as implement and have the Weapon Expertise Heavy Blade feat, does the +1 apply to implement attacks as well?
When you use your weapon as an implement you get the following bonuses:
The enhancement bonus from the magical enchantment
The benefit of any expertise feat that includes the term "implement"
Anything else that applies specifically to "attacks" made through or with that weapon (rogue can use sneak attack with a light blade implement)
You do not get benefits from the following bonuses:
The weapon's proficiency bonus (+2/+3)
The benefit form a expertise feat that specifies weapon.
Any benefits that specifically specify weapon attacks.
If you have a character that plans to use a weapon as both an implement and a weapon it is a good idea to look at the new expertise feats published in Dragon 402 which include limited use expertise feats for both weapon and implement powers (or generic attacks).
From what I recall, no. Weapon expertise and implement expertise are different. Weapon expertise grants the bonus when you use the weapon to do physical damage with the weapon, such as a melee basic attack. Implement expertise gives you a bonus when you use the weapon as an implement for an attack, such as eldritch blast.