Yes, you can drop your weapon (free), ready a new one (move), and attack (standard), all in the same turn. However, if you're switching between a reach weapon and a one-handed weapon, you can actually do better than that:
Two-Handed Weapons: What kind of action is it to remove your hand from a two-handed weapon or re-grab it with both hands?
Both are free actions. For example, a wizard wielding a quarterstaff can let go of the weapon with one hand as a free action, cast a spell as a standard action, and grasp the weapon again with that hand as a free action; this means the wizard is still able to make attacks of opportunity with the weapon (which requires using two hands).
Therefore, you can remove your main hand from the reach weapon (free), ready a one-handed weapon (move), and attack (standard). When you want to use the reach weapon again, you can sheathe the backup weapon (move), put both hands back on the reach weapon (free), and attack (standard). You can switch between weapons and attack in the same turn, without needing to drop either.
Yes, opponents provoke an attack of opportunity if they pass through your threatened space:
Provoking an Attack of Opportunity: Two kinds of actions can provoke attacks of opportunity: moving out of a threatened square and performing certain actions within a threatened square.
Moving: Moving out of a threatened square usually provokes attacks of opportunity from threatening opponents. There are two common methods of avoiding such an attack—the 5-foot step and the withdraw action.
Note that this applies any time they leave a threatened square, regardless of whether they move toward you, away from you, or side to side. It's especially dangerous to move near somebody with reach from size or a spiked chain, since you can't easily escape with a 5-foot step or withdraw action.