Lots of things going on here.
You are getting the weird voltages because you are measuring across all hots. If you measure between any of the wires in your box to the box itself (this assumes the box is grounded correctly) you should get close to 120v.
So yes to your first question, you can use the exact same wiring to connect your dimming switches with a couple of caveats.
Make sure your dimmers and LEDs are compatible. Check the packaging or Google it.
Add a grounding wire. (See Below)
The dimming switch does not require a neutral (common in smart switches)
You are going to have to be careful wiring up your lights. That white wire coming into your switch box is HOT, not a neutral. You should wrap it, and the other end, in black E-tape, to mark it. Make sure your chain of LEDs are wired in parallel with the Red or Black wire as the hot, and what should be a different white wire (probably found in the same box as the other end of the 14/3). If you have more questions about the wiring of the LEDs please post pictures of the lighting wiring or start a new question.
based on the photo you do not need to change any wiring. When adding fixtures to the Red wire, Run 14/2 from this box and continue to each subsequent fixture (you can and should daisy chain). In the box pictured connect the black wire to the red wire and blue wire (blue is the fixture in your pic). Then add the white wire of the new 14/2 to the 4 already twisted together. It looks like there is already a 14/2 running from this box to the other fixture. So you dont need to add a wire, just continue chaining 14/2 to that system of fixtures tying all the hots together and all the white/neutrals together. The last fixture of each chain will only have one 14/2 going to it.