Yes. Meshes, curves, text and metaballs with a glowing material can carry a halo. When the emission is set as a value on an Emission or Principled BSDF node, the halo's brightness follows the emission strength and the object's size; when it comes from a texture or a node link, set the halo's Brightness by hand.

Yes. Use the Stylised types, or switch any rainbow to Artistic mode and pick a palette. Raise Opacity for solid, painted bands.

Yes. Reveal grows the bow with one click, every setting can be keyframed, and a bow linked to the sun follows the lamp when you animate it.

That is the physics. The bow sits 42° from the point opposite the sun, so when the sun is higher than about 42° the primary bow is below the horizon. Lower the sun, or turn off Clip at Horizon to see the full circle, as you would from a plane.

No. A rainbow is a light mesh with an emission shader. It is rebuilt only when its settings or the things it follows change (the linked sun, or a halo's light and camera), and it adds very little to render times.

The positions, colours and brightness of the bows come from a spectral model of light in water drops that was checked against exact Mie scattering: bow positions within 0.05° for raindrops and 0.2° for fog, peak brightness within 2%, colours within 0.01 in CIE xy, and the inner glow and secondary bow within about 10% (light reflected off the outside of the drops is left out). The gallery images compare renders with photographs taken at the same sun height.