Ghișeul de bagaje pierdute este deschis.

Because -ul is the Romanian definite article attached to the end of the noun.

• ghișeu = a counter / a desk
• ghișeul = the counter / the desk

Romanian usually puts the at the end of the noun instead of before it, unlike English.

A good approximation is gee-SHEH-ool.

A few helpful points:

• gh before i keeps a hard g sound, like in go
• ș sounds like sh
• -ul is the attached definite article, pronounced roughly ool

So: ghi-șe-ul.

Here de links the main noun to what it is for or associated with.

So ghișeul de bagaje pierdute literally means something like:

• the counter of lost luggage
• more naturally in English: the lost luggage counter

Romanian often uses de where English would use a noun-noun combination, like luggage counter or passport control desk.

Romanian commonly uses bagaje in the plural where English often uses the uncountable noun luggage.

So:

• bagaj = baggage / a piece of luggage depending on context
• bagaje = luggage / bags / baggage

In this sentence, bagaje pierdute means lost luggage.

Because pierdute agrees with bagaje.

• pierdut = masculine singular
• pierdută = feminine singular
• pierduți = masculine plural
• pierdute = feminine/neuter plural

Bagaje is a neuter plural noun, and in Romanian, neuter nouns behave like feminine in the plural. So the adjective must be pierdute.

That is a very common Romanian pattern: neuter nouns use masculine forms in the singular and feminine forms in the plural.

So:

• singular: bagaj pierdut
• plural: bagaje pierdute

This is one of the most important things to know about Romanian neuter nouns.

Because deschis agrees with ghișeul, not with bagaje.

The subject of the sentence is ghișeul, and ghișeu is a neuter singular noun. In the singular, neuter nouns take masculine agreement, so the correct form is deschis.

So:

• ghișeul ... este deschis = correct
• deschisă would be for a feminine singular noun
• deschise would be for a plural noun

Este means is. It is the 3rd person singular form of a fi = to be.

So the structure is:

• Ghișeul = the counter
• este = is
• deschis = open

Together: The lost luggage counter is open.

In a full normal sentence, este is standard and expected.

On signs, notices, or in very short labels, Romanian may sometimes be more compressed, but the full sentence form is still:

Ghișeul de bagaje pierdute este deschis.

So for learning purposes, it is best to keep este.

No, this is the normal Romanian order:

subject + verb + adjective

• Ghișeul de bagaje pierdute = subject
• este = verb
• deschis = predicative adjective

Also notice that inside the noun phrase, Romanian usually places descriptive adjectives after the noun:

• bagaje pierdute = lost luggage

That is very typical in Romanian.

Not exactly in every context.

Ghișeul de bagaje pierdute specifically suggests a counter for lost luggage, especially in a travel setting such as an airport or station.

A more general lost and found office is often:

• biroul de obiecte pierdute

So this sentence is more specifically about lost baggage/luggage services, not necessarily every kind of lost property.