Yes, the strength of the reflection is dependent on Fresnel (which depends on the IOR/spec-mask of the material), and the reflections are added over all the other shading, not multiplied.
The trees do reflect green, it's just that the reflection there is quite weak compared the the amount of red light that's also coming for those areas, so the subtle green appears washed out in the camera. Keep in mind that the objects in that image are probably objectively 1000 times darker than the sky, when it comes to measuring them as light sources, so in the reflection, you can only really make out the sky and silhouettes of objects blocking the sky.
Car paint is actually very complex to simulate realistically. The most basic version is a white (colourless) specular reflection added over a Lambert diffuse surface -- which represents the wax/clear-coat, and the underlying surface.
In a more involved shader, you've got several different specular reflections -- the clear-coat, the surface of the paint, and microscopic metal flakes (in metallic paints). The first one will be white, but the other specular reflections may be coloured.
------- clear coat -------- paint -------- + x \ / - x flecks of coloured metals suspended in the paint -------- more paint -------- opaque primer -------- underlying metal surface (not visible)