Jejich pas je platný.

Jejich means their.

In this sentence, it shows who the passport belongs to: their passport.

A useful thing to know is that jejich is one of the Czech third-person possessive forms that does not change its ending. So unlike words such as můj / moje / moje or náš / naše, jejich stays jejich.

Examples:

• jejich pas = their passport
• jejich auta = their cars
• jejich dcera = their daughter

Pas means passport.

It is a masculine inanimate noun in Czech. In this sentence, it is in the nominative singular, because it is the subject of the sentence: the passport is what is valid.

So:

• pas = passport
• masculine inanimate
• nominative singular here

Je means is.

It is the 3rd person singular present tense of the verb být (to be).

So:

• já jsem = I am
• ty jsi = you are
• on/ona/ono je = he/she/it is

Because pas is singular, Czech uses je:

• Jejich pas je platný. = Their passport is valid.

If the subject were plural, you would use jsou:

• Jejich pasy jsou platné. = Their passports are valid.

Platný is an adjective meaning valid.

It has the form platný because it must agree with pas, which is:

• masculine
• singular
• nominative

So the adjective also appears in the masculine singular nominative form:

• platný pas = a valid passport
• pas je platný = the passport is valid

Compare:

• jízdenka je platná = the ticket is valid
  (jízdenka is feminine)
• vízum je platné = the visa is valid
  (vízum is neuter)
• pasy jsou platné = the passports are valid
  (plural)

That is a very common question, because many Czech possessive words do change.

For example:

• můj pas
• moje kniha
• moje auto

But jeho, její, and jejich are different: they are normally indeclinable in this use, so they do not change their form.

So you get:

• jejich pas
• jejich kniha
• jejich auto
• jejich pasy

The noun and adjective change when needed, but jejich stays the same.

Normally, yes: jejich means their, referring to more than one person.

So:

• jeho pas = his passport
• její pas = her passport
• jejich pas = their passport

In standard learner Czech, the safest understanding is that jejich refers to several people.

Because the sentence is talking about one passport that belongs to them.

This works the same way as in English:

• their passport = one passport
• their passports = more than one passport

So:

• Jejich pas je platný. = Their passport is valid.
• Jejich pasy jsou platné. = Their passports are valid.

Whether singular or plural is used depends on the thing possessed, not on the number of possessors.

The sentence Jejich pas je platný. is a normal, neutral word order.

Czech word order is quite flexible, so other versions are possible, but they change the emphasis.

For example:

• Jejich pas je platný. = neutral
• Platný je jejich pas. = emphasizes valid
• Pas je jejich platný. = not natural in this meaning

So the given sentence is the most straightforward way to say it.

No, not in a normal present-tense sentence like this.

Czech does sometimes omit forms of to be in special styles such as headlines, notes, or very informal fragments, but in a regular full sentence you should say:

• Jejich pas je platný.

Without je, it would sound incomplete to a learner and usually unnatural in ordinary speech.

A rough pronunciation guide is:

YEH-yikh pahs yeh PLAHT-nee

A few important details:

• j in Czech sounds like English y
• ch is the throaty sound in Scottish loch or German Bach
• á is a long vowel
• ý is also long, so platný ends with a long -ný

Word by word:

• Jejich ≈ YEH-yikh
• pas ≈ pahs
• je ≈ yeh
• platný ≈ PLAHT-nee

Yes. Platný is exactly the normal word for something that is valid, in force, or not expired.

It is very commonly used with documents such as:

• platný pas = a valid passport
• platné vízum = a valid visa
• platná jízdenka = a valid ticket
• platný řidičský průkaz = a valid driver’s license

So Jejich pas je platný. sounds completely natural.