1. There is only one winch on the mast. With a cutter rig, how do you raise 3 sails with only one winch?
My mast has three winches so no, normally one winch per halyard unless you're just sailing a sloop rig, then two winches. Is there rigging to lead the halyards to the cockpit? Some boats have this instead to make raising and lowering the main easier when not passage-making.
2. The mast is Lefeill (I believe) it has two tracks aft. One obviously for the mainsail, the other, I'm guessing for a trysail?
Correct, the starboard offset track is for a trysail.
The lug gate on the mainsail track is below the boom. The boom's gooseneck is fitted into the sail track. In order to remove the mainsail the boom has to be lowered past the lug gate and could possibly come out at an inopportune time.
Is this a normal configuration?
Yes you have to lower it to remove it but it should be secured to the mast with two hex bolts above the lug gate at the gooseneck. The nice thing about handling the boom is you can secure it to the gallows so you have a pendulum to assist in removing the boom from the track. Easy peasy.