Der Kasus in diesem Satz ist leicht zu erkennen.

Because Kasus is a masculine noun in German. In the nominative singular, masculine nouns normally take the article der, so:

• der Kasus = nominative
• den Kasus = accusative
• dem Kasus = dative
• des Kasus = genitive

In this sentence, der Kasus is the subject, so nominative is the correct case.

The subject is der Kasus.

You can test this by asking What is easy to recognize?
Answer: The case.

So the basic structure is:

• Der Kasus = subject
• ist = finite verb
• leicht zu erkennen = predicate
• in diesem Satz = prepositional phrase giving context

Because the preposition in is taking the dative here.

German prepositions like in can take:

• dative for location: in this sentence
• accusative for direction/movement: into this sentence

Here there is no movement. It means inside / within this sentence, so German uses the dative.

Since Satz is masculine singular, the dative form of dieser is diesem:

• nominative: dieser Satz
• dative: in diesem Satz

Many masculine and neuter nouns in German do not add a visible ending in the dative singular when they already have an article or determiner.

So:

• der Satz
• in dem Satz
• in diesem Satz

Older or more formal German sometimes adds -e in the dative for certain nouns, but that is mostly outdated in everyday language. So in diesem Satze would sound old-fashioned.

This is a very common German pattern:

• sein + adjective + zu + infinitive

So:

• ist leicht zu erkennen

literally means something like:

• is easy to recognize
• can be recognized easily

It is similar in meaning to English easy to recognize.

Other examples:

• Das ist schwer zu erklären. = That is hard to explain.
• Der Fehler ist leicht zu finden. = The mistake is easy to find.

Because zu + infinitive usually goes to the end of the clause in German.

Here:

• ist is the conjugated verb
• zu erkennen is an infinitive phrase that belongs at the end

That is very normal German word order.

So the sentence frame is:

• Der Kasus in diesem Satz ist ... zu erkennen.

with the infinitive erkennen placed at the end.

Because leicht is a predicate adjective here, not an adjective directly in front of a noun.

Compare:

• ein leichter Satz = an easy sentence
  
  • adjective before a noun, so it gets an ending
• Der Satz ist leicht. = The sentence is easy
  
  • predicate adjective after ist, so no ending

In ist leicht zu erkennen, leicht is also a predicate adjective, so it stays leicht.

Not formally, no.

A true passive would be:

• Der Kasus kann leicht erkannt werden.

But Der Kasus ... ist leicht zu erkennen has a very similar meaning. It is often called a passive-like or modal construction.

So:

• ist leicht zu erkennen
• kann leicht erkannt werden

are close in meaning, though not exactly the same grammatical structure.

Because they are nouns, and all nouns are capitalized in German.

So in this sentence:

• Kasus = noun
• Satz = noun

Words like ist, leicht, zu, and erkennen are not nouns, so they are not capitalized.

A learner can reasonably wonder about that, because German allows this kind of placement.

In practice, it is understood as giving the context in this sentence: the case is easy to recognize in this sentence.

You can think of it as answering:

• Where is the case easy to recognize?
  In this sentence.

At the same time, it sits right after der Kasus, so it also feels closely connected to that noun phrase. German is comfortable with this kind of structure, and native speakers will understand it naturally.

Yes. In grammar, Kasus and Fall can both mean grammatical case.

So you could also say:

• Der Fall in diesem Satz ist leicht zu erkennen.

However, Kasus sounds more technical and grammatical, while Fall is the more traditional everyday grammar term.

So:

• Kasus = more linguistic/technical
• Fall = also correct, often more familiar in school grammar

The sentence follows normal German main-clause word order:

• Der Kasus in diesem Satz = first element
• ist = finite verb in second position
• leicht = predicate adjective
• zu erkennen = infinitive phrase at the end

So the pattern is basically:

• Subject + verb + predicate + infinitive

That is why the sentence sounds completely natural in German.