Should the inline protector be placed under the antenna, on the duplexor, or should I actually add a connection where the wire enters the building and place it there?
Direct lightning strike isn't the only thing you need to be concerned about. Even nearby strikes can induce enough energy into your feed line to cause damage.
For this reason, it's standard practice to put the lightning protector where the coaxial cable enters the structure. After all, the structure (home) is what you are trying to protect.
Can the inline protector be hooked up to the same line as the line grounding the mast?
Yes, but you need to look at your grounding as an entire system.
The mast needs to be well grounded at the base. This is to give a direct path for lightning to ground. You want that energy to go straight down the mast to the ground.
Since your mast will likely be a little ways away from your home, and your protector should be mounted where the coax enters the home, you should ground the protector below that point. That should be a straight run of heavy copper cable straight down to the ground with a ground rod there. Again, you want a straight and short run for the energy to ground.
All the grounds need to be at a same potential, for this reason, the NEC says that all your grounds need to be bonded. This would mean that the ground rod(s) at the tower base need to be connected to the ground rod at the house electrical panel. The protector and it's ground needs to be bonded to this also.
The idea is you need to get the lightning strike, or any induced energy, into the ground as quickly as you can. You want to give it a direct path, and you need to make sure all the grounds are connected to make a ground system.
The other thing you need to do is ground the coax shield in a couple of places. Industry standard is to ground the coax shield to the mast near the antenna, then again at the bottom. If you were running a taller tower, you'd do this every 100 feet or so.
Is this actually going to be able to handle a direct hit or will this only protect it from nearby strikes?
Depends on how well everything works.
If you are using a DC grounded antenna that is well connected to the mast, your coax shield is grounded at the top and bottom of the mast, you have a good ground rod system, low resistance ground, a good protector that is properly grounded, then you may survive a strike. Broadcast towers are hit all the time and they don't get knocked off the air. Mountain top repeater sites git hit directly or suffer nearby hits frequently as well.
The trick is to make the ground path though your ground system more attractive than going through your radio.
Doesn't mean that some energy will make it to your radio. It happens.
Based on what you are saying about lightning strikes hitting nearby, and that you are putting up a mast taller than the trees, I think you run the risk of taking a hit.
That would suggest that it might be a real good idea to talk to a professional and see what they can do for you. Not getting it right could result in damage to your home. There are other steps you may need to take, like installing a lightning terminal above your antenna, a better network of ground rods under the mast, etc. They'll also have the equipment to test the soil resistance to determine exactly what you'll need.
Even making your mast lower than the trees will not necessarily protect you.
A good place to study this is by finding a copy online of Motorola R56. It's a well written document that covers system/site grounding.