There are two questions in here.
One is "Can I apply Weapon Finesse to the off-end of a double weapon?" The other is "Can I use a double weapon as a double weapon without attacking with both ends?"
Treating double weapons as a combination of one-handed and light shows up in two places in the PHB. (This may be clarified in the Rules Compendium, BTW - anyone have it yet?)
1. Equipment. A character can fight with both ends of a double weapon as if fighting with two weapons, but he or she incurs all the normal attack penalties associated with two-weapon combat, just as though the character were wielding a one-handed weapon and a light weapon. The character can also choose to use a double weapon two handed, attacking with only one end of it.
2. Power Attack. Normally, you treat a double weapon as a one-handed weapon and a light weapon. If you choose to use a double weapon like a two-handed weapon, attacking with only one end of it in a round, you treat it as a two-handed weapon.
Now, both places imply that if you're only using one end, it's considered a two-handed weapon; this argues that in order to treat it as one-handed and light, you will incur TWF penalties, even if you end up not making a second attack (just as if you began a full attack with two shortswords, but stopped after one attack).
As far as Weapon Finesse goes, it depends on how one reads Power Attack.
Y'see, the Equipment excerpt doesn't say to treat the double weapon as one-handed and light for all purposes; it says to treat it as such for purposes of the normal attack penalties associated with two-weapon combat. The normal attack penalties are -6/-10; relieved by 2/2 if the off-hand weapon is light; relieved by 2/6 if you have the TWF feat. Nothing else is a 'normal attack penalty associated with two-weapon combat'; for example, the -4 penalty to Disarm checks for using a light weapon is not a penalty associated with two-weapon combat. It's a penalty that's completely independent of whether you're engaged in two-weapon combat or not.
The Power Attack text makes no such distinction. It just says "Normally, you treat a double weapon as a one-handed weapon and a light weapon." So the decision that needs to be made is whether or not this text is globally applicable, or only applicable in the context of Power Attacking.
Either way, it means you can't apply Power Attack to the off-end (treated as light), and the main end only gains 1-for-1 from Power Attack (considered a one-handed weapon).
But if we consider it to be specific to Power Attack, certain other things apply to double weapons:
1. They gain +4 to Sunder and Disarm checks with either end, rather than +0/-4; since this modifier is neither a normal penalty associated with two-weapon combat nor in the context of Power Attack, the weapon is not treated as a one-handed and light combination; thus, it is a two-handed weapon.
2. The primary end adds 1.5x Str bonus to damage; since Str bonus is neither a normal penalty associated with two-weapon combat nor in the context of Power Attack, the weapon is treated as a two-handed weapon. The off-end may deal 1.5x Str bonus (as a two-handed weapon) or .5x Str bonus (as an off-hand attack); this will require the DM's judgement to resolve (as in the situation of a lance wielded in the off-hand while mounted.)
3. The weapon cannot be used while grappling or swallowed whole.
4. The weapon cannot be used with Weapon Finesse.
If we treat the Power Attack text as globally applicable, it's different:
1. The primary end (as a one-handed weapon) incurs no modifier to Sunder or Disarm checks; the off-end (as a light weapon) takes a -4 penalty.
2. The primary end (as a one-handed weapon) adds 1x Str bonus to damage; the off-end adds .5x (as an off-hand attack).
3. In theory, the off-end can be used while grappled or swallowed whole; however, since one may not fight with two weapons while grappling, it could be argued that the weapon must be treated as two-handed, and thus one cannot treat the off-end as light, rendering it unusable.
4. The off-end of the weapon can be used with Weapon Finesse.
-Hyp.