Odpovědní arch musíme odevzdat moderátorovi.

Not in this phrase. In odpovědní arch, odpovědní means something like answer- or for answers, so the whole expression means answer sheet.

This is a set expression used in tests, competitions, and quizzes. So you should learn odpovědní arch as one phrase, not as responsible sheet.

In other contexts, forms of odpovědný can of course mean responsible, for example odpovědní lidé = responsible people.

It is in the accusative singular, because it is the direct object of odevzdat: it is the thing being handed in.

• co musíme odevzdat? → odpovědní arch

The noun arch is masculine inanimate, and for masculine inanimate nouns the accusative often looks the same as the nominative. That is why arch does not change form here.

Because it agrees with arch in gender, number, and case, and in this combination the form happens to stay the same.

So here you have:

• arch = masculine inanimate singular
• case = accusative
• odpovědní matches it

For this type of adjective, the nominative and accusative singular can look identical, so odpovědní arch stays odpovědní arch.

Because moderátorovi is in the dative singular.

The verb odevzdat often works with:

• a direct object in the accusative = what is handed in
• an indirect object in the dative = to whom it is handed in

So:

• odpovědní arch = the thing being handed in
• moderátorovi = the person receiving it

In other words:

• komu? → moderátorovi

Because Czech usually leaves out subject pronouns when the verb ending already makes the subject clear.

Musíme means we must / we have to, so my is unnecessary.

You could say My musíme odevzdat moderátorovi odpovědní arch, but that would add emphasis, something like We have to hand it in.

Because after a modal verb like muset (must / have to), Czech normally uses the infinitive.

So:

• musíme = we must
• odevzdat = hand in

Together:

• musíme odevzdat = we must hand in

This is very similar to English grammar:

• we must hand in not
• we must handed in

Because odevzdat is perfective. It describes a completed action: handing something in as a finished act.

That fits this sentence well, because handing in an answer sheet is usually a single completed event.

Compare:

• odevzdat = hand in, submit completely, once
• odevzdávat = be handing in, hand in repeatedly, habitually, or as an ongoing process

Examples:

• Musíme odevzdat arch do pěti minut. = one completed submission
• Každý týden odevzdáváme úkoly. = repeated action

Because Czech word order is flexible, and putting odpovědní arch first gives it extra prominence.

The original sentence highlights the answer sheet, roughly like:

• As for the answer sheet, we have to hand it in to the moderator.

A more neutral order would be:

• Musíme odevzdat odpovědní arch moderátorovi.

Both are grammatical. The difference is mainly in emphasis and information structure, not basic meaning.

Yes, very often.

For example, these are all possible in the right context:

• Musíme odevzdat odpovědní arch moderátorovi.
• Odpovědní arch musíme odevzdat moderátorovi.
• Moderátorovi musíme odevzdat odpovědní arch.

The case endings show who is doing what to whom, so Czech can move words around more freely than English can.

Still, the word order is not random. Different orders sound more neutral, more emphatic, or more contrastive depending on context.

Because Czech has no articles.

So arch can mean a sheet, the sheet, or sometimes just sheet, depending on context.

In this sentence, the situation usually makes it clear that a specific answer sheet is meant, so English would often translate it with the:

• the answer sheet

But Czech does not need a separate word for that.