Brama do ogrodu jest dziś zamknięta.

Because do requires the genitive case.

The basic dictionary form is ogród = garden.
After do, it changes to ogrodu.

• ogród = nominative
• ogrodu = genitive singular

So brama do ogrodu means gate to the garden.

Here do means to in the sense of leading to or connected with a place.

So:

• brama do ogrodu = gate to the garden
• literally: gate to/of access to the garden

This is a very normal Polish pattern:

• klucz do drzwi = key to the door
• droga do miasta = road to the city

Because it agrees with brama, and brama is a feminine noun.

In Polish, adjectives and adjective-like forms must match the noun in:

• gender
• number
• case

So:

• brama = feminine singular
• therefore: zamknięta = feminine singular

Compare:

• brama jest zamknięta = the gate is closed
• dom jest zamknięty = the house is closed
• okno jest zamknięte = the window is closed

It is originally a passive participle from the verb zamknąć = to close / to shut / to lock, but in sentences like this it works very much like an adjective.

So jest zamknięta means is closed.

Learners often find it easiest to think of it as an adjective in this kind of sentence, because it behaves like one and agrees with the noun.

In a normal full sentence, jest is the standard form and should be used:

• Brama do ogrodu jest dziś zamknięta.

In very informal speech, notes, signs, or headlines, Polish sometimes drops jest, for example:

• Brama do ogrodu dziś zamknięta.

But for a learner, the safest standard version is with jest.

Yes, Polish word order is fairly flexible.

Brama do ogrodu jest dziś zamknięta is a natural, neutral sentence.
But you could also say:

• Dziś brama do ogrodu jest zamknięta.
• Brama do ogrodu dziś jest zamknięta.

The meaning stays basically the same, but the emphasis changes slightly.

• starting with dziś puts extra focus on today
• the original version sounds smooth and neutral

Yes. Both mean today.

• dziś = shorter, very common
• dzisiaj = slightly fuller form, also very common

So these are both correct:

• Brama do ogrodu jest dziś zamknięta.
• Brama do ogrodu jest dzisiaj zamknięta.

No. They are different.

• brama = gate, usually larger, often an outside entrance
• drzwi = door
• furtka = a small gate, often for people walking through

So brama do ogrodu suggests a gate leading into the garden, not a house door.

Usually closed is the safest translation here.

Depending on context, zamknięta can sometimes also imply shut or even locked, but by itself it does not always clearly mean locked with a key.

If Polish wants to be more specific, it may say:

• zamknięta na klucz = locked with a key
• zaryglowana = bolted/barred

So in this sentence, the most natural understanding is simply:

• The gate to the garden is closed today.

A rough English-friendly guide:

• dziś sounds approximately like jish or jeesh, but softer and shorter
• the final ś is a soft sh-like sound

A few key pronunciation points in the whole sentence:

• brama = BRA-ma
• ogrodu = o-GRO-du
• jest = roughly yest
• dziś = soft jish
• zamknięta = roughly zam-KNYEN-ta

The cluster knię in zamknięta can be tricky at first, but you will get used to it with repetition.