Pošta je vpravo od náměstí a pekárna je vlevo.

They mean to the right and to the left.

• vpravo = to the right / on the right
• vlevo = to the left / on the left

They are adverbs of place or direction, so they describe where something is.

In this sentence:

• Pošta je vpravo od náměstí = The post office is to the right of the square.
• pekárna je vlevo = the bakery is to the left.

Because od means from, and Czech often expresses this idea as to the right from/of something.

So:

• vpravo od náměstí = to the right of the square
• literally: right from the square

This is a very common pattern:

• vlevo od školy = to the left of the school
• naproti od...? No — that one works differently, so don’t copy this pattern everywhere.

For vpravo and vlevo, od + genitive is normal.

It is in the genitive case, because it follows od.

The dictionary form is also náměstí, and in the singular the nominative and genitive look the same, so you do not see a spelling change here.

• nominative: náměstí
• genitive: náměstí

So even though the form does not change, the case still does.

Because náměstí is a neuter noun of a type whose singular nominative and singular genitive are identical.

This is very common with many neuter nouns ending in -í.

So:

• to je náměstí = that is a square
• od náměstí = from/of the square

Same form, different grammatical role.

Because Czech, like English, can leave out repeated information when it is obvious from context.

The full version would be:

• Pošta je vpravo od náměstí a pekárna je vlevo od náměstí.

But since od náměstí is already understood, Czech naturally shortens the second clause to:

• a pekárna je vlevo

This sounds normal and natural.

A means and.

It joins the two clauses:

• Pošta je vpravo od náměstí
• a pekárna je vlevo

So it simply connects two pieces of information.

Je is the 3rd person singular of být (to be), meaning is.

• Pošta je... = The post office is...
• pekárna je... = the bakery is...

Czech often repeats the verb in coordinated clauses, just as English usually does:

• The post office is... and the bakery is...

You could not normally omit je here.

It can mean either, depending on context.

Common meanings:

• pošta = post office
• pošta = mail / post

In this sentence, because it is describing a location in town, it clearly means the post office.

Because Czech does not have articles like the and a/an.

So:

• Pošta can mean the post office or a post office
• pekárna can mean the bakery or a bakery

The exact meaning depends on context. In a sentence like this, English usually uses the because the places are treated as known landmarks.

Yes, Czech word order is fairly flexible, but some versions sound more neutral than others.

The original sentence is natural and neutral:

• Pošta je vpravo od náměstí a pekárna je vlevo.

You could also say:

• Vpravo od náměstí je pošta a vlevo je pekárna.

This version puts more focus on the locations first: To the right of the square is the post office, and to the left is the bakery.

So yes, the word order can change, but the emphasis changes too.

Yes, those forms also exist and are common:

• napravo = on the right / to the right
• nalevo = on the left / to the left

In many everyday situations, vpravo/vlevo and napravo/nalevo are close in meaning.

Examples:

• Pošta je vpravo od náměstí.
• Pošta je napravo od náměstí.

Both can work. For a learner, it is good to recognize both pairs, but the sentence you were given uses vpravo and vlevo.

A simple approximate pronunciation is:

Pošta je vpravo od náměstí a pekárna je vlevo.
POSH-ta ye VPRAH-vo ot naa-MNYES-tyee a pe-KAAR-na ye VLEH-vo

A few useful notes:

• š sounds like sh in shoe
• je sounds roughly like ye
• á is a long vowel
• ě affects the sound before it, so mě sounds roughly like mnye
• vlevo begins with vl-, which may feel unusual to English speakers, but Czech allows that cluster

Yes, it is natural and idiomatic.

It is a normal way to describe where places are in relation to a town square or another landmark. The omission of od náměstí in the second clause is also completely natural, because it avoids unnecessary repetition.

A fully explicit version is possible, but the given sentence sounds very normal.