A whip does not threaten, and so therefore, you would not be able to threaten the range of the whip.

You would, however, be able to threaten within 5 feet of you, since you can use any part of your body to deliver a touch spell, and so therefore can threaten at normal melee range. If something did provoke an AoO, you would only be able to deliver the touch spell via hand, not with your whip.

A whip does not threaten, and so therefore, you would not be able to threaten the range of the whip, regardless of having a touch spell available, whether or not you can channel it via the whip. Nothing about being able to channel touch spells into a whip changes the (lack of) ability of the whip to threaten.

The rule noted, about "Armed" Unarmed attacks, specifically only applies to unarmed or natural attacks. While the whip does not threaten, it is a weapon, and does not count at all as being unarmed. Therefore, this exemption does not apply to the whip.

You would, however, be able to threaten within 5 feet of you, since you can use any part of your body to deliver a touch spell, and so therefore can threaten at normal melee range, even if wielding other weapons. This threatening would not be with the whip, though. If something did provoke an AoO, you would only be able to deliver the touch spell via an unarmed attack, not with your whip.