Pod dveřmi je průvan.

Because Czech dveře is a plural-only noun. Even when English says door, Czech usually uses the grammatically plural word dveře.

So:

• dveře = a door / doors
• dveřmi = by/with/under the door, in the instrumental plural

This is normal Czech, not a special meaning. So pod dveřmi still means under the door, not necessarily under the doors.

Dveřmi is instrumental plural.

The preposition pod can take different cases depending on meaning:

• pod + instrumental = location, under/below
• pod + accusative = movement to a position under something

Here the sentence describes a location, not movement, so Czech uses the instrumental:

• Pod dveřmi je průvan. = The draft is under the door / There is a draft under the door.

Then pod would normally take the accusative.

For example:

• Strčil papír pod dveře. = He pushed the paper under the door.

Here pod dveře uses the accusative because something is moving to a position under the door.

So the contrast is:

• pod dveřmi = under the door, already there
• pod dveře = under the door, moving there

Because the subject is průvan, and průvan is singular.

In this sentence:

• Pod dveřmi = a prepositional phrase saying where
• je = is
• průvan = the subject, a draft

So the verb agrees with průvan, not with dveřmi.

That is why Czech uses:

• je průvan = there is a draft

not jsou.

Yes. Czech does not need a dummy subject like English there.

English says:

• There is a draft under the door.

Czech simply says:

• Pod dveřmi je průvan.

Literally, it is closer to Under the door is a draft, but in natural English the meaning is There is a draft under the door.

This is a very common Czech pattern:

• Na stole je kniha. = There is a book on the table.
• V pokoji je ticho. = It is quiet in the room / There is silence in the room.

Because Czech has no articles.

So průvan can mean:

• a draft
• the draft

The exact meaning depends on context. In this sentence, English would most naturally say a draft, but Czech does not mark that with a separate word.

Průvan is:

• masculine inanimate
• nominative singular in this sentence

It is nominative because it is the grammatical subject of je.

So:

• průvan = subject
• je = agrees with it in singular

Yes, but in normal usage it usually means through the gap at the bottom of the door.

So the idea is not just that something exists in a spot below the door in a geometric sense. It usually means the draft is coming from under the door.

That is exactly the kind of phrase Czech uses in everyday speech.

Yes, Czech word order is flexible, but the version you have is very natural.

• Pod dveřmi je průvan. = neutral, natural when the location is the starting point
• Průvan je pod dveřmi. = possible, but more marked; it can sound like you are emphasizing the draft

Czech often puts the known setting first and the new information later. So Pod dveřmi je průvan is a typical way to introduce what is there.

A few helpful points:

• Czech stress is usually on the first syllable of each word:
  • POD dveřmi je PRŮvan
• ů in průvan is a long vowel, like a long oo
• ř in dveřmi is the famous Czech sound with no exact English equivalent

A practical learner-friendly guide:

• pod ≈ pot with a clear d
• dveřmi = stress on dve-; the ř is the difficult sound
• průvan ≈ proo-van

If you cannot say ř perfectly yet, that is completely normal.

Dveřmi is the standard form.

You may also hear:

• pod dveřma

That is a common colloquial instrumental plural form in spoken Czech. It is natural in everyday conversation, but in careful or written standard Czech, dveřmi is preferred.

So:

• pod dveřmi = standard
• pod dveřma = colloquial spoken Czech