Ráno piji čaj z velkého hrnku, ale moje sestra má raději kávu.

Yes. In this sentence, ráno means in the morning / in the morning time.

Czech often uses ráno without a preposition when talking about something that happens in the morning in a general sense:

• Ráno piji čaj. = I drink tea in the morning.

You may also see expressions like:

• dnes ráno = this morning
• každé ráno = every morning

So here ráno functions as a time adverb.

Yes, both are possible.

• piji is a standard/spisovná form
• piju is also very common in everyday speech

Both mean I drink.

The verb is pít = to drink. Its first-person singular forms are commonly given as:

• piji
• piju

So:

• Ráno piji čaj.
• Ráno piju čaj.

Both are correct.

Yes, čaj is the direct object of piji, so it is in the accusative case.

The reason it still looks like čaj is that for many masculine inanimate nouns, the nominative and accusative singular are the same.

So:

• nominative: čaj = tea
• accusative: čaj = tea (same form)

That is why you do not see a change here.

Because the preposition z requires the genitive case.

So:

• hrnek = mug
• after z, it becomes z hrnku = from/out of a mug

The adjective must agree with the noun in case, number, and gender, so:

• velký hrnek = a big mug (nominative)
• z velkého hrnku = from/out of a big mug (genitive)

That is why both words change:

• velký → velkého
• hrnek → hrnku

Literally, yes, z velkého hrnku means from a big mug or out of a big mug.

In Czech, pít z něčeho is a normal way to say that you drink something from a cup, glass, mug, bottle, and so on.

Examples:

• pít z hrnku = to drink from a mug
• pít ze sklenice = to drink from a glass
• pít z láhve = to drink from a bottle

English might sometimes focus more on the container as location, but Czech usually uses the idea of drinking from the container.

Ale means but.

It connects the two parts of the sentence:

• Ráno piji čaj z velkého hrnku
• ale moje sestra má raději kávu

So the whole sentence contrasts two preferences:

• I drink tea in the morning
• but my sister prefers coffee

This is very similar to English but.

Yes, historically/literally it is something like that, but in modern Czech the expression mít raději means:

• to prefer
• to like something better

So:

• moje sestra má raději kávu = my sister prefers coffee

It is a very common Czech way to express preference.

Other examples:

• Mám raději čaj než kávu. = I prefer tea to coffee.
• Máš raději léto, nebo zimu? = Do you prefer summer or winter?

So it is best learned as a fixed expression: mít raději + object.

Because kávu is the accusative singular form of káva.

Here, coffee is the thing being preferred, so it is the direct object of má raději.

• nominative: káva = coffee
• accusative: kávu = coffee as an object

This is different from čaj, which did not visibly change because its nominative and accusative are the same.

Compare:

• Káva je horká. = Coffee is hot.
  (káva = subject, nominative)

• Mám rád kávu. = I like coffee.
  (kávu = object, accusative)

Yes, Czech could often say just sestra if the context makes it clear whose sister it is.

But moje sestra is perfectly natural and can add clarity or emphasis:

• sestra = sister
• moje sestra = my sister

Czech often omits possessives when ownership is obvious, but it does not have to.

So all of these can be natural depending on context:

• Moje sestra má raději kávu.
• Sestra má raději kávu.

The version with moje is simply more explicit.

Czech word order is more flexible than English word order, because case endings show grammatical function. But that does not mean all word orders sound equally natural in every context.

The given sentence is very natural:

• Ráno piji čaj z velkého hrnku, ale moje sestra má raději kávu.

You could also hear variations such as:

• Čaj piji ráno z velkého hrnku...
• Moje sestra ale má raději kávu.

These may change emphasis slightly.

In general:

• earlier position often gives known/background information
• later position often gives new or emphasized information

So the original sentence is a good neutral version for a learner.

Sestra is in the nominative singular, because it is the subject of the verb má.

In the second clause:

• moje sestra = the person doing the action
• má raději = prefers
• kávu = the thing preferred

So:

• sestra = nominative
• kávu = accusative

Here are the main dictionary forms:

• ráno = morning
• pít = to drink
• čaj = tea
• z = from, out of
• velký = big
• hrnek = mug
• ale = but
• můj = my
• sestra = sister
• mít = to have
• raději = rather / preferably / more gladly
• káva = coffee

Useful full chunks to remember:

• pít čaj = to drink tea
• pít z hrnku = to drink from a mug
• mít raději kávu = to prefer coffee

Yes, they matter a lot in Czech.

For example:

• ráno
• piji
• čaj
• velkého
• má
• raději
• kávu

Czech spelling is quite consistent, and the accents are part of the correct written form. They can affect pronunciation and sometimes meaning.

For a learner, it is a good idea to treat them as essential, not optional.