Wet Dry or a drip leg as required by most civilized codes
The trap should be before the vent. The trap is used to maintain a watter barrier to prevent waste water and sewer gasses from entering the home. The vent is use after the trap to allow the water to flow freely in the pipe with out drawing the water from the trap.
Some municipal building codes allow it, but most do not. You should use smooth rigid metal vent pipe (typically aluminum) instead.
It needs aleast a 2 in. pipe. tubs are 1.5 in.
A direct vent appliance uses a two pipe system which takes combustion air from the outside through one pipe, and then exhausts flue gases out the other pipe. These system do not use room air for the combustion process.
computer says no
Use a Plumber's "snake".
No, it won't carry the required amount of air. A vent is usually 1.5 inch and an exhaust is 4 or 5 inch.
water pipe
It depends upon the venting that is used, look for your vent pipes on the roof and see if any are close to open windows. If you find a particularly close vent pipe (and you home has several vent pipes) you can add a "Studor Vent" to the top of the vent. A Studor vent is the equivalent to a one-way air valve that only allows air to pass, or be drawn, into the pipe, so that sewer gases will be greatly reduced. You don't even have to use pipe cement/adhesive to secure the Studor Vent.
Mainly for making water pipe.
Vacuum away all lint. Brush inside of vent to free any stubborn lint. Use a blower to determine if vent is clear all the way through.
When you cannot use B vent to find a way to vent the HWT through to the roof!