Learn Hardcore Russian: Осторожно, не бросай мяч в окно! - Careful, don’t throw the ball at the window!

Осторожно literally means carefully / cautiously, but very often it’s used like a standalone warning: Careful! / Watch out!
In this sentence it functions almost like an interjection (a warning word) introducing the command.

Why is there a comma after Осторожно?

The comma separates the warning (Осторожно) from the imperative clause (не бросай...). In writing, this is a common way to show a brief pause, like: Careful, don’t...

Why does Russian use не бросай and not не брось?

This is an aspect choice in the negative imperative:

не бросай (imperfective) = don’t throw (in general / don’t do that), often a prohibition or repeated/ongoing warning.
не брось (perfective) = don’t throw (this one time, right now, don’t let it happen), more momentary and less common in everyday prohibitions.

Both can be possible, but не бросай is the “default” for Don’t do that.

How is the imperative бросай formed?

бросай is the singular informal imperative from бросать (imperfective to throw).
Very roughly: infinitive броса-ть → imperative броса-й → бросай.
For the formal/plural imperative, you use бросайте.

Is this sentence addressing one person or more than one person?

не бросай is 2nd person singular informal (you to one person you’re on ты terms with).
If you’re speaking to:

multiple people, or
one person formally (вы), you’d say: Осторожно, не бросайте мяч в окно!

Why is мяч in the form мяч (not changed)?

мяч is the direct object of бросать (to throw what?), so it’s accusative.
For masculine inanimate nouns, the accusative is usually the same as the nominative, so it stays мяч.

Why is it в окно and not в окне?

With в:

в + accusative answers where to? and indicates motion/direction (into / toward): в окно
в + prepositional answers where? and indicates location (in): в окне

Since throwing involves movement toward a target, Russian uses в + accusative: в окно.

But окно looks identical in nominative and accusative—how can I tell the case?

For many neuter nouns ending in -о, the nominative and accusative are identical: окно → окно.
You identify the case by the context and the preposition:

в окно after a motion verb strongly signals accusative (direction).

Does в окно mean “into the window” or “through the window”?

In Russian, в окно can cover what English might split into:

at the window (as a target), and often by implication
through the window (e.g., tossing something so it goes in via the opening)

If you need to be explicit about “through,” Russian might use other wording, but in everyday speech бросить/бросать в окно is the normal way to say throw it through the window / out the window (via the window opening) depending on context.

Why is не used here—are there any special rules for negating imperatives?

не is the standard negation for imperatives: не + imperative = don’t + verb.
ни is used in different structures (e.g., emphatic negation), not for a normal command like this.

What does the exclamation mark add? Could it be a period instead?

The exclamation mark emphasizes urgency/emotion—this reads like a sharp warning.
A period (Осторожно, не бросай мяч в окно.) would sound calmer, more like a neutral instruction.

How would I soften this command to sound more polite?

Common options:

Add пожалуйста: Осторожно, не бросай мяч в окно, пожалуйста.
Use the formal/plural form: Осторожно, не бросайте мяч в окно.
Use a gentler phrasing like a suggestion: Давай не будем бросать мяч в окно. (Let’s not throw the ball at/through the window.)