Yes. Say for instance a creature in melee casts a spell that requires a ranged touch attack, it would provoke two attacks of opportunity, one for the casting of the spell and one for the ranged attack in melee.

You still can make only one attack of opportunity for each opportunity that your foe gives you. For example, if you have Combat Reflexes and a Dexterity score of 15 you can make up the three attacks of opportunity each turn. You could make all three of them against the same foe, provided that the foe does three different things that provoke attacks of opportunity. (Link)

While the example from the article doesn't specify the situation I've outlined above it clearly states that though each individual opportunity does not provoke more than once, you can make multiple attacks against a creature provided they offer multiple opportunities.

There's no attack of opportunity.

This is a case of specific-beats-general. Improved Disarm is unambiguous:

You do not provoke an attack of opportunity when you attempt to disarm an opponent.

Yes, disarming is a melee attack (disarm rules say that you do it "as a melee attack", not "instead of a melee attack" or similar), and an unarmed disarming attack is an unarmed melee attack. But the character is performing an unarmed melee attack as an attempt to disarm an opponent, and Improved Disarm clearly states that this doesn't provoke an attack of opportunity.