Does using scent to “note the direction” provoke an attack of opportunity

Sorry, one movement only provokes one AoO from a given defender.

See the d20pfsrd:

If you have the Combat Reflexes feat, you can add your Dexterity modifier to the number of attacks of opportunity you can make in a round. This feat does not let you make more than one attack for a given opportunity, but if the same opponent provokes two attacks of opportunity from you, you could make two separate attacks of opportunity (since each one represents a different opportunity). Moving out of more than one square threatened by the same opponent in the same round doesn't count as more than one opportunity for that opponent. All these attacks are at your full normal attack bonus.

So if you shriek "SERPENTINE!!!" and run circles around your opponent, they still only get one "leaving a threatened square" AoO on you.

The opportunity from Hold the Line is different, but only works once upon them entering your threatened area. So you would get only one from Hold the Line and one for them leaving a threatened square.

Note that the leaving a threatened square is per round - not even just per turn - with the Mythic rules in use in our WotR campaign we've been finding a lot of cases where you get to act multiple times in a round, even charge multiple times, etc. If by hook or crook someone charged you, ran off, charged you again, and ran off again over the course of a round (on their turn or across multiple turns), you would still only get 1 AoO for them leaving your threat but could get multiple from Hold the Line, if they actually leave and enter your threatened area with a charge twice. Up to the limit of the number of AoOs you have.

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.