Veterinář myje psovi tlapku a vidí dlouhé drápy.

Because Czech often uses the dative of possession with body parts, especially when someone is doing something to that body part.

So Veterinář myje psovi tlapku is literally something like The vet is washing the dog a paw, but naturally it means The vet is washing the dog's paw.

This pattern is very common in Czech:

• myje psovi tlapku
• čistí dítěti zuby
• myje si ruce

Using a possessive form such as psovu tlapku is possible in some contexts, but here psovi tlapku sounds more natural and idiomatic.

Pes is an irregular-looking noun because its stem changes in oblique cases.

Its forms include:

• nominative: pes
• genitive: psa
• dative: psovi or psu
• accusative: psa
• instrumental: psem

So psovi is the dative singular form of pes. The e disappears and the stem becomes ps- in most cases.

Here is the breakdown:

• Veterinář = nominative singular
  The subject, the one doing the actions.

• psovi = dative singular
  The dog, understood as the possessor/affected participant.

• tlapku = accusative singular
  The direct object of myje.

• drápy = accusative plural
  The direct object of vidí.

This is a very typical Czech pattern: subject in nominative, main object in accusative, and sometimes an additional dative noun.

Because tlapku is the accusative singular of tlapka.

Tlapka is a feminine noun ending in -a, and for many nouns of that type:

• nominative singular: tlapka
• accusative singular: tlapku

Since the paw is the thing being washed, Czech uses the accusative:

• myje tlapku

Because the adjective has to agree with the noun in gender, number, and case.

• drápy is plural
• the noun dráp is masculine inanimate
• here it is in the accusative plural

For masculine inanimate nouns, the accusative plural looks the same as the nominative plural, so:

• dlouhé drápy

That is why you do not get dlouhý here.

Both are 3rd person singular present tense verb forms.

• myje = he/she/it washes / is washing
• vidí = he/she/it sees

In this sentence, the subject is veterinář, so both mean:

• the veterinarian washes
• the veterinarian sees

Both verbs are in the present tense, and both describe what the same subject is doing.

Because once the subject is clear, Czech usually does not repeat it unnecessarily.

So:

• Veterinář myje psovi tlapku a vidí dlouhé drápy.

naturally means:

• The veterinarian washes the dog's paw and sees long claws.

Repeating the subject would be possible, but it would usually sound unnecessary:

• Veterinář myje psovi tlapku a veterinář vidí dlouhé drápy.

Czech often leaves repeated subjects out when they are obvious.

No, Czech word order is flexible, but not random.

The given sentence has a neutral, natural order:

• Veterinář myje psovi tlapku a vidí dlouhé drápy.

You could rearrange parts of it, for example:

• Veterinář psovi myje tlapku a vidí dlouhé drápy.
• Psovi veterinář myje tlapku a vidí dlouhé drápy.

But changing the order usually changes the focus or emphasis, not the basic meaning.

So the original sentence is a good neutral version.

Good question, because the form drápy can look like either nominative plural or accusative plural.

We know it is the object because of the structure of the sentence:

• the subject Veterinář has already been established
• vidí means sees, and it normally takes something seen as its object
• dlouhé drápy is what the veterinarian sees

So even though the form itself is ambiguous, the syntax and meaning make it clear.

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

So Czech often says simply:

• Veterinář
• tlapku
• drápy

and context tells you whether English should use a, the, or no article at all.

If Czech wants to be more explicit, it can use words like ten, but that is not required here. In a normal sentence like this, no article is needed.