Brake weirdness on my new E-bike I very recently purchased an E-bike for commuting to work and other area locales. I understand with any new bicycle there will be some break-in time and after a few rides I did notice the brakes were a bit softer than when they started out. I looked online and found some basic tips to adjust the the brake tension which worked.

The brakes on the bike are TekTro Aries mechanical discs.

The weirdness begins with a slight ticking noise I recently started to hear when riding and goes away when I actuate the brakes. However, when I tried to duplicate the problem at home to confirm the problem, I found it difficult to recreate. With the rear wheel lifted off the ground, I turn the wheel and no ticking sound. Additionally while still holding the wheel off the ground, actuating the brake handle had no noticeable effect on stopping the rotation of the wheel. I then put the tire back in contact with the ground and actuate the brake handle, wheel refuses to budge until I release the brake.

Can anyone explain to me how to clear up the ticking noise?

Is the brake not working with the tire off the ground normal?
You seem to have tested the rear wheel. Have you tested whether the front wheel and brake are making the noise? 

Also are you pulling the correct lever to operate the rear brake? It depends which country the bike was built in as to which one operates the rear brake. So in the UK the left hand lever operates the rear brake but in the rest of Europe (I believe)its the right hand lever. If you are pulling the front brake lever then obviously the rear wheel will not stop spinning. With the bike on the ground pulling either brake lever will stop the bike moving.

Ticking can be the rotor disc very slightly touching one of the pad. It can be a tick once-per-rotation of the disc if the disc is slightly warped at one point. The ticking would stop when the brake was pulled on as the pads would fully engage and make other louder noises.