Do misky dávám vodu a krmím štěně.

Because do requires the genitive case in Czech.

The basic dictionary form is miska (bowl), but after do it changes to misky:

• miska = bowl
• do misky = into the bowl

So Do misky means into the bowl.

Here do means into or to the inside of.

It is used when something moves or is placed inside something:

• do misky = into the bowl
• do domu = into the house
• do tašky = into the bag

So in this sentence, the water is being put into the bowl, not just near it or on it.

Because voda is the direct object of dávám, so it has to be in the accusative case.

• voda = water (nominative, dictionary form)
• vodu = water (accusative)

So:

• Dávám vodu = I am putting/giving water

This is a very common pattern in Czech: the thing directly affected by the verb often goes into the accusative.

Because Czech usually leaves out subject pronouns when they are obvious from the verb form.

• dávám = I put / I am putting
• krmím = I feed / I am feeding

Both verb endings already show that the subject is I, so já is not necessary.

You could say Já dávám vodu a krmím štěně, but it would usually sound more emphatic, as if you were stressing I.

Dávám is the 1st person singular present tense of dávat.

So it means:

• I give
• I put
• I am putting

In this sentence, dávat has the sense of putting/giving water into the bowl.

Also, dávat is imperfective, so it often suggests an ongoing, repeated, or habitual action depending on context.

It can mean either, depending on context.

Czech present tense with an imperfective verb often covers both:

• I put water into the bowl
• I am putting water into the bowl

So this sentence could describe:

1. something happening right now, or
2. something someone regularly does

Context tells you which meaning is intended.

Yes, Dávám vodu do misky is also correct.

Czech word order is more flexible than English, because case endings show grammatical roles. That means word order is often used for focus or emphasis, not just grammar.

• Do misky dávám vodu puts early focus on where the water is going.
• Dávám vodu do misky is a very natural neutral order too.

So the original sentence is correct; it just highlights into the bowl a bit more.

Because štěně is a neuter noun, and in the singular its nominative and accusative forms are the same.

• štěně = puppy (nominative)
• štěně = puppy (accusative)

So although it is the direct object of krmím, its form does not change here.

This is normal for many neuter nouns in Czech.

Because krmit takes a direct object in the accusative.

So:

• krmím štěně = I am feeding the puppy

The form štěněti is dative, and that would not normally be used after krmit.

Compare:

• Dávám vodu štěněti. = I am giving water to the puppy
  
  • here štěněti is dative, because the puppy is the recipient
• Krmím štěně. = I am feeding the puppy
  
  • here štěně is the direct object, so accusative is used

Krmím means I feed or I am feeding.

It comes from the verb krmit = to feed.

So:

• krmím psa = I am feeding the dog
• krmím kočku = I am feeding the cat
• krmím štěně = I am feeding the puppy

Like dávám, it is 1st person singular present tense.

A simply means and.

It joins the two actions:

• dávám vodu = I am putting water
• krmím štěně = I am feeding the puppy

Since both verbs have the same subject (I), Czech does not need to repeat anything else.

So the sentence is literally structured like:

• Into the bowl I put water and feed the puppy.

No. Czech does not have articles like a/an/the.

So miska or misky does not by itself tell you whether English should use:

• a bowl
• the bowl

That has to come from context.

The same applies to štěně:

• a puppy
• the puppy

Czech leaves that distinction unstated unless something else in the sentence makes it clear.

Yes. Depending on what you want to stress, Czech might also use a more specific verb such as nalévám (I pour).

For example:

• Do misky nalévám vodu. = I am pouring water into the bowl.

But dávám vodu do misky is still perfectly natural and common. It is a bit broader, like I put/give water into the bowl.