I bleed my brakes today and I'm not able to get my pistons to extend. They are current retracted, but nothing gets them back out even with the air bubbles removed. Also, the brakes have no tension. I made this video that reveals what the issue and what I did. Please provide advice.
You're bleeding them wrong.
Tektro has been making decent hydros, but the clarity of their published bleed procedures has still left a lot to be desired, so I don't blame you.
Their published instructions differ a little across models, but what I do for most of them is put a bleed block in, position them such that the port on the lever is the highest point and the port on the caliper is the lowest point, put a syringe on each end (starting with the new fluid in the caliper end), and push the fluid up while applying gentle back pressure on the lever syringe plunger. This is where you'll see most of your bubbles. Then if what came out is dirty, I remove and drain the lever syringe, replace it, refill the caliper syringe, and repeat until I'm getting clean looking fluid all the way through. Then I push it back and forth a few times, keeping the syringes upright to collect the air. You could bonk on the caliper and lever with a soft tool to loosen bubbles if you want, but I typically find it not necessary. When you're not getting any more bubbles in either direction, remove the syringe from the caliper end first and close the port tight, then the lever end. Once both ends are sealed, squeeze the lever with the bleed block still in, and it should be rock solid. I never actuate the brake lever before this with Tektros.
If you only have one syringe (the Tektro consumer kit only comes with one), I believe you do it by setting up a collection bag at the lever end and pushing fluid up from the caliper, but to be honest I never do it this way so I may be missing something.
No bike brakes today are bled without a bleed block in place between the pistons. You don't want the pistons able to move around during the bleed process because then the fluid will be overfilled and your pad gaps will be all screwed up. You can improvise one by cramming whatever in there and holding it in with tape or a rubber band. Or, in most cases a Shimano block of the same pad type will go right in too.
Actuating the lever like you're doing in the video with the caliper bleed port still open is going to cause the exact behavior you're seeing of shooting fluid out of the bleed port without moving the pistons. The pistons have some resistance to overcome from the seals etc, but the fluid will move freely. There's not really a circumstance I can think of where it makes sense to squeeze the lever with the caliper bleed port open.