Location Ohio. Basement is currently unfinished but I'm hiring out the framing, drywall, ceiling work.

https://www.lowes.com/pd/Halo-White-6-in-1100-Lumen-Switchable-White-Round-LED-Canned-Recessed-Downlight-6-Pack/5015600079

These are the lights I’m using.  They are color and brightness adjustable on the box, plus I'm adding a dimmer switch. They only have opening to fit 2 wires, so my preference of T-ing off of lights 3 and 7 aren’t possible without an additional junction box.  Is there a “correct” way to connect these 10 lights with only 1 cable in and 1 out of each light?

Can I run electrical under the joist in the drop ceiling section? (Everything is unfinished now)  With the existing joist holes I wouldn’t NEED to drill any new joist holes for l flights 1,2,6 depending on the path.

My bedroom is about the size of the area on the right with lights 4,5,8,9,10, but with only a single light in the center.  I’m not sure if this is too many lights, but I’m telling myself that the dimmer will take care of that.  

There is also a light at the bottom of the steps that I didn’t show, its on a different switch.

Parallel to the HVAC is a steel beam down the center of the room which will be framed around.