Wysokość przeszkody jest mała.

Because przeszkody is in the genitive case.

In Polish, when you say the height of something, the thing after height usually goes into the genitive:

• wysokość budynku = the height of the building
• wysokość stołu = the height of the table
• wysokość przeszkody = the height of the obstacle

So this is the pattern:

• wysokość
  • genitive noun = height of ...

The basic dictionary form is przeszkoda.
Here it changes to przeszkody because it means of the obstacle.

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

In Polish, adjectives must match the noun they describe in:

• gender
• number
• case

Here:

• wysokość = feminine singular
• so the adjective must also be feminine singular
• therefore: mała

Compare:

• mały dom = a small house
• mała przeszkoda = a small obstacle
• małe okno = a small window

Even though przeszkody is nearby, mała does not describe przeszkody. It describes wysokość.

Because wysokość is a noun meaning height.

This sentence is built like:

• The height of the obstacle is small.

So Polish uses a noun phrase:

• Wysokość przeszkody = the height of the obstacle

If you wanted a different structure, you could also say something like:

• Przeszkoda jest niska. = The obstacle is low.

That is grammatically possible, but it is not exactly the same focus.
The original sentence talks specifically about the height as a measured property.

In normal standard Polish, jest is usually kept in sentences like this.

• Wysokość przeszkody jest mała.

This is the verb być (to be) in the 3rd person singular: jest = is.

Unlike in some other Slavic languages, Polish normally does use the present-tense form of to be.

Omitting it would usually sound:

• incomplete,
• very informal,
• poetic,
• or like a note/headline rather than a full sentence.

So for a learner, the safe rule is:

• use jest in normal statements like this.

Yes, and many speakers may actually find niska more natural in some contexts.

Both can work, but the nuance is a bit different:

• mała wysokość = small height
• niska wysokość = low height

In English, we often prefer low with height, and Polish often does something similar with niski / niska / niskie.

So:

• Wysokość przeszkody jest mała. = correct
• Wysokość przeszkody jest niska. = also correct, often very natural

A learner should understand both. The version with mała emphasizes that the height is small in amount.

The subject is Wysokość przeszkody.

More specifically:

• head noun: wysokość
• dependent genitive noun: przeszkody

So the sentence is not mainly about the obstacle as the subject. It is about the height of the obstacle.

That matters because the predicate adjective agrees with the head noun:

• wysokość is feminine
• therefore mała is feminine

No, Polish word order is more flexible than English word order.

The neutral, standard order is:

• Wysokość przeszkody jest mała.

But other orders are possible for emphasis, for example:

• Mała jest wysokość przeszkody.
• Jest mała wysokość przeszkody. (less natural in ordinary speech)

Even though different orders are possible, the original version is the most natural for a simple textbook sentence.

So for learners:

• use Wysokość przeszkody jest mała as the default pattern

Good question. In Polish, many feminine nouns end in -a, but not all of them.

Nouns ending in -ość are typically feminine, for example:

• wysokość = height
• długość = length
• szybkość = speed
• jakość = quality

So even without -a, wysokość is feminine, and that is why the adjective is mała.

A rough English-friendly guide is:

• Wysokość ≈ vih-SO-koshch
• przeszkody ≈ pshe-SHKO-dih
• jest ≈ yest
• mała ≈ MA-wa

A few useful sound notes:

• w sounds like English v
• rz usually sounds like zh as in measure
• sz sounds like sh
• ł sounds like English w
• ść is a soft cluster that is tricky for beginners; something like a soft shch is a decent approximation

You do not need perfect pronunciation immediately, but ł = w is especially important here in mała.

Because Polish has no articles like English a/an/the.

So:

• przeszkoda can mean an obstacle or the obstacle
• wysokość przeszkody can mean the height of an obstacle or the height of the obstacle

The exact meaning depends on context.

That is very normal in Polish. Learners coming from English often look for the, but Polish simply does not mark it this way.

Yes.

Przeszkoda can mean:

• a physical obstacle, barrier, hurdle
• a difficulty or impediment in a more abstract sense

For example:

• To nie jest przeszkoda. = That is not an obstacle / That is not a problem.
• Były pewne przeszkody. = There were some obstacles/difficulties.

In your sentence, because it talks about height, the meaning is clearly a physical obstacle.