Webkamera musí být nad monitorem.

Because webkamera is the subject of the sentence — it is the thing that must be somewhere.

In Czech, the subject is normally in the nominative case.
The basic dictionary form is webkamera, and that is the form used here.

Also, webkamera is a feminine noun, which you can often guess from the ending -a.

Because the preposition nad requires the instrumental case when it means location, as in above.

So:

• monitor = nominative
• monitorem = instrumental singular

In this sentence, nad monitorem means above the monitor, so Czech uses the instrumental after nad.

Not always.

With nad, the case depends on whether you are talking about:

• location → usually instrumental
• movement toward a position → usually accusative

Examples:

• Webkamera je nad monitorem. = The webcam is above the monitor.
  → location, so instrumental
• Pověsil kameru nad monitor. = He hung the camera above the monitor.
  → movement/direction, so accusative

So in your sentence, it is instrumental because it describes where the webcam should be.

Because musí is a modal verb meaning must / has to, and modal verbs are followed by an infinitive.

Here:

• musí = must
• být = to be

So literally, the structure is:

• webkamera = webcam
• musí být = must be
• nad monitorem = above the monitor

This is very similar to English must be.

No, that would be incorrect.

After musí, you need a verb in the infinitive. In this sentence, that infinitive is být.

So:

• Webkamera musí být nad monitorem. = correct
• Webkamera musí nad monitorem. = incorrect

Czech sometimes omits forms of to be in the present tense in certain sentence types, but not after a modal verb like musí.

Yes, but it means something different.

• Webkamera je nad monitorem. = The webcam is above the monitor.
  This simply states a fact.
• Webkamera musí být nad monitorem. = The webcam must be above the monitor.
  This expresses necessity, rule, or requirement.

So the difference is not grammar only — it changes the meaning.

No, Czech word order is fairly flexible, but the usual neutral order here is:

Webkamera musí být nad monitorem.

You can change the order for emphasis, for example:

• Nad monitorem musí být webkamera.
  Emphasis on the location
• Musí být nad monitorem webkamera.
  More marked, less neutral

Even though these are possible, the original version is the most natural neutral sentence for a learner to use.

Because Czech does not have articles like English a and the.

So monitor can mean:

• a monitor
• the monitor

The exact meaning depends on context.

In nad monitorem, English usually needs above the monitor, but Czech simply uses the noun without an article.

A simple guide:

• musí ≈ moo-see
• být is harder, because ý is a long vowel not exactly like English. A rough learner approximation is something like beet, but that is not perfect.

A few useful notes:

• í in musí is long
• ý in být is also long
• Czech stress is usually on the first syllable:
  • MU-sí
  • BÝT

Monitor is a masculine inanimate noun.

Yes, that matters, because the noun’s gender affects its case endings.
Here, in the instrumental singular, monitor becomes monitorem.

So the ending -em is part of how this masculine noun changes in the instrumental.

Yes. It is a commonly used Czech word, even though it is based on an English borrowing.

It behaves like a regular Czech feminine noun:

• nominative: webkamera
• genitive: webkamery
• dative: webkameře
• accusative: webkameru
• instrumental: webkamerou

So even borrowed words are often fully adapted to Czech grammar.