How to measure the correct belt drive tension?
As to measuring belt tension, the tool is your best option. If you own the bike, then you should own the tool. 

Without it, however, place an S-bent spoke or similar wire in a hook over the center of the top of the belt. Add weight to the bottom hook. 10 pounds is the spec. Yes, this is a lot of weight for a bent spoke. Be creative. Or buy the tool.

Place a ruler next to the belt, at the point of the weight's pull. Write down the measurement.

Remove the weight. Measure again, in the same place. Subtract the first measurement from the second measurement. The difference should be between 5 and 12 millimeters. 10 millimeters is ideal.

The alignment is dependent on the type of dropout. 

EDIT 1: The image below is a new tool from Gates, called the Eco Tension Tester, which does exactly as described above, in a more professional manner. Perhaps it will help describe the intent of the method I described.



With the dropout style you posted in your image, the alignment is actually set with two things. 


Wheel centering - the wheel needs to be equally centered between the chainstays. This is a do it by eye and feel job, although you can gauge your success by measuring from the rim's brake surface to the inside surface of your chainstay, assuming your wheel is properly dished over your hub.
The second thing which affects the belt alignment on the pulley is your "chain" line. With the District, this alignment is set with the length of the bottom bracket spindle. The more perfect the chainline, the less likely you will have issues with the belt rolling off the cogs. Most bike shops have a tool like the Park Tool CLG-2 for measuring chainline accurately, although it is designed to work with a toothed cog.




If you have consistent issues with the belt rolling off the cog, and your dropouts are evenly set up in the frame, and your wheel is centered, find an LBS to check your chainline.

You may need to swap the bottom bracket axle to get more perfect chainline, in order to solve this issue. Assuming the bike has not had the BB replaced by you, it may be wise to ask the shop where it was purchased whether it is the original BB, and whether they will help with any chain line issues under warranty status.

EDIT 2: It actually appears that belt "alignment" issues are directly related to belt tension with the Gates Carbon Drive belts. If the tension is correct, they track well. If it is too low, they will track toward the frame. Too high tracks away from the frame.

I hope that is helpful.