Learn Farsi: در حالی که او قهوه را خنک می‌کند، من فرآیند را تماشا می‌کنم، هرچند دیر است. - While he cools the coffee, I watch the process, even though it is late.

هرچند (even though) can be followed by either the indicative or the subjunctive. Because the lateness is a stated, objective fact in this context, the indicative است is used. If it were a hypothetical situation like 'even if it were late', you would use the subjunctive باشد.

What is the difference between خنک می‌کند used here and خنک می‌شود?

خنک می‌کند (from خنک کردن) means 'cools something down' (an action done to an object), which is why we see the direct object marker را after the coffee. If the coffee were cooling down on its own, you would use خنک می‌شود (from خنک شدن - to become cool).

Does در حالی که always refer to time passing?

It usually refers to two continuous actions happening at the same time ('while'), as it does here. However, just like the English word 'while', it is also frequently used to mean 'whereas' to show a contrast between two situations.

Is فرآیند a common word to use here?

Yes, فرآیند (farayand) is the standard word for a 'process'. It is very common when describing a step-by-step procedure, showing the speaker is paying close attention to how the coffee is being prepared.