Does this use solar powered batteries?

No batteries. This is completely solar powered.

Will this fit in a velux tlr 14" ridgid sun tunnel?

Yes this product will fit in all Velux rigid model Sun Tunnels. It will also work in other brands of tubular skylights with rigid tunnels that you can remove the interior lens from. The product comes with a small hanger clip. To install remove the interior Sun Tunnel lens, connect the hanger clip at a tube joint 1 to 2 feet up inside the tunnel, remove the plastic tab at the battery to activate the night light (Note: will light up if you place your hand over the solar panel) and hang the light from the clip and re-install the interior lens. The light will automatically come on in low light conditions.

Can I put two solar lights into a single tube? If so, how it it impact the daytime light output?

You should be able to, depending on the diameter of your tube. I have both a 14" tunnel and a 9" tunnel, with a night light in each, and even the 9 inch could fit at least 3, probably 4 of these if you wanted to. But I only have one per tube. With one, the regular sunlight output during the day is not visibly impacted at all. I doubt you'd have a noticeable change with two either. At night, a single night light casts a soft blue-ish light that's just bright enough to be able to see the immediate area clearly without turning on a lamp, yet not so bright that it'll disturb your ability to sleep in any way.

Planning to install model #thr0140000, 1) will this product works with this? 2) what is the color of the light, i need soft yellow, is it possible?

I am not sure who manufactures that model of tube light but if it has a rigid tunnel and you can remove the interior lens you should be able to install it as it simply hangs inside the unit by a clip installed at a tunnel joint location. For the color of the light I would say it is probably closer to White but the interior lens on the skylight diffuser will also have an effect on the color of light