Learn Hardcore French: Quand il étudiait chaque soir, son niveau progressait vite. - When he studied every evening, his level was improving quickly.

Because the sentence describes habitual or ongoing actions in the past: studying every evening (étudier) and his level improving over time (progresser). The imparfait in French is used for repeated or continuous past events, background descriptions, and habits, not for isolated, completed actions.

How do you decide between the imparfait and the passé composé in a past-time sentence like this?

Use the imparfait for background actions, habits, or states in the past. Use the passé composé for single, completed events. Here, both studying and improving are ongoing/habitual, so you stick with the imparfait. If you wanted to say He studied last night and his level improved quickly, you’d use the passé composé: Il a étudié hier soir et son niveau a progressé vite.

What nuance does starting the sentence with quand give? Can you start differently?

Starting with quand (meaning when) followed by the imparfait emphasizes that two past, habitual actions happened simultaneously: whenever he studied each evening. You could also place the time clause later without changing the core meaning:
Son niveau progressait vite quand il étudiait chaque soir.

Is the comma necessary after the subordinate clause introduced by quand?

Yes. When a subordinate clause comes first, French typically uses a comma before the main clause. It clarifies the break:
Quand il étudiait chaque soir, son niveau progressait vite.

Could we use lorsque instead of quand? Any difference?

Yes. Lorsque is more formal or literary but functions the same way as quand in temporal clauses. Both take the indicative for factual or habitual past statements.

Could we invert the order: Son niveau progressait vite quand il étudiait chaque soir? Does it change anything?

You can invert the clauses without altering the essential meaning. The sentence still expresses that his level improved quickly at the times he studied each evening. The emphasis slightly shifts toward his progress.

Could we use tous les soirs instead of chaque soir? Also, why is the noun singular after chaque?

Yes, tous les soirs (“every evening”) and chaque soir (“each evening”) are often interchangeable. With chaque, the noun remains singular: chaque jour, chaque soir, etc. If you use tous, the noun is plural with an article: tous les soirs.

Why is it son niveau and not sa niveau? How do possessive adjectives agree here?

Possessive adjectives in French agree with the gender and number of the noun possessed, not the possessor. Since niveau is masculine (le niveau), you use son regardless of the possessor’s gender.

Why use vite instead of rapidement? Are they interchangeable?

Both vite and rapidement mean quickly. Vite is more colloquial and common in spoken French; rapidement is more formal or written. They’re interchangeable in meaning, with a slight difference in register.