Is it possible to dual wield with a double weapon and a off-hand weapon? For example, I'm wanting to use a double-sword in my main hand and, in my off hand, a handaxe.
To use the Double Weapon you have to have it in both of your hands (it's too heavy to wield effectively in one hand). So if you want to attack with the double sword, you have to have both hands on it.
If all you want to do is pull a hand off the double weapon, pull and chuck a hand axe, and then put your hand back on the double weapon, yeah you can totally do that. If you're working with a power like say...Throw and Stab, then yes, you can use this strategy (free to take hand off sword, minor to pull hand axe, standard to throw, free to put hand back on, then stabby. Alternatively you can take the Quick Draw feat to save your action economy.
Seeing your comment about your character concept though, I'd go straight sword and board here. Basically take your longsword, and have it be a longsword mechanically (1d8, +3 prof bonus, enchanted as a longsword etc), but when you describe it in game, when you think about it etc, it's the double sword your thinking of. This is 100% supported and endorsed by the rules, and is the recommended out for issues like this.
No, double weapons take both hands. This is not as obvious as it could be in the original version of the Adventurer's Vault, where they were introduced, but Wizards has cleared this up with errata.
There's a new sidebar for Double Weapons (page 2 of the linked errata), which explicitly says:
Waxeagle has a good point about being able to throw a handaxe with your off-hand while still holding the double weapon in your main hand.
To be doubly clear, you can't attack with a double weapon unless you're wielding it in both hands. You can hold a double weapon in one hand while you have something else in the other, like a shield or handaxe, but you can't actually use (attack with) the double weapon unless you are using both hands for wielding it and nothing else.