Scheinen is usually used for light sources or light itself emitting or appearing (the sun shines, the light shines). Leuchten means to shine, to glow, to give off light, often with a nuance of glowing or being bright in itself (a lamp glows, eyes glow).
Das Licht leuchtet durch das Fenster is understandable but sounds slightly odd, because the light itself is the thing that is already emitted; we usually say Das Licht scheint durch das Fenster or Die Lampe leuchtet.
No. In this sentence, scheint is the main verb, and durch is a preposition that belongs with das Fenster (durch das Fenster).
There is a separable verb durchscheinen (to shine through), where you could say Das Licht scheint durch. That is a different structure: durch in that case is a separable prefix of the verb, not a preposition.
The ch in Licht is a soft, front sound, often called the ich‑Laut, made with the tongue near the hard palate (similar to the h in English hue, but stronger and hissier).
In durch, many speakers use a sound closer to the ich‑Laut too, but some use a slightly more dark/back variant (between the ich‑Laut and the Bach sound). It is never pronounced like the ch in English chair.
Each preposition changes the meaning:
For the idea that light passes from one side to the other, durch das Fenster is the natural choice.