Na macie do ćwiczeń jest mało przestrzeni.

Macie is the locative singular form of mata (mat).

After the preposition na when it means on, Polish usually uses the locative case:

• mata = mat
• na macie = on the mat

So:

• Na macie = on the mat

This is one of the basic case changes that English speakers need to get used to in Polish.

Do ćwiczeń means for exercise, for exercising, or for workouts/exercises.

It is made of:

• do = for / for the purpose of / for
• ćwiczeń = exercises

The noun ćwiczenia means exercises. After do, Polish uses the genitive case, so:

• ćwiczenia → ćwiczeń

So mata do ćwiczeń literally means something like:

• a mat for exercises
• in more natural English: an exercise mat

Because the preposition do requires the genitive case.

The dictionary form is:

• ćwiczenie = exercise

Plural nominative:

• ćwiczenia = exercises

But after do, it changes to the genitive plural:

• do ćwiczeń = for exercises

This pattern is very common in Polish:

• kubek do kawy = a cup for coffee
• buty do biegania = shoes for running
• sprzęt do ćwiczeń = exercise equipment

Because mało works like a quantity word meaning little / not much, and after it Polish usually uses the genitive.

So:

• mało przestrzeni = little space / not much space

By contrast:

• mała przestrzeń = a small space

These are related, but not identical.

Compare:

• Tu jest mało przestrzeni. = There is little space here.
• To jest mała przestrzeń. = This is a small space.

So in your sentence, the focus is on insufficient amount of space, not just the size as a simple adjective-noun combination.

Here przestrzeni is in the genitive singular.

The base form is:

• przestrzeń = space

After mało, Polish typically uses the genitive:

• mało czasu = little time
• mało wody = little water
• mało miejsca = little room
• mało przestrzeni = little space

So even though przestrzeni can also look like other case forms in other contexts, in this sentence it is best understood as genitive singular.

Jest is singular because the sentence is built as an existential statement: there is little space.

In Polish, mało often behaves like a singular quantity expression, so jest mało... is normal:

• Jest mało czasu. = There is little time.
• Jest mało miejsca. = There is little room.
• Jest mało przestrzeni. = There is little space.

So the structure is not really about matching an ordinary subject in the same way English learners might expect. It functions more like:

• there is little X

Yes, jest is the 3rd person singular form of być (to be), and here it works like there is in English.

So:

• Na macie do ćwiczeń jest mało przestrzeni.

can be understood structurally as:

• On the exercise mat there is little space.

Polish often uses jest in this kind of existence/location sentence.

Yes. Polish word order is more flexible than English, although different orders can sound more or less natural depending on emphasis.

Your sentence:

• Na macie do ćwiczeń jest mało przestrzeni.

A possible alternative:

• Jest mało przestrzeni na macie do ćwiczeń.

Both are understandable. The difference is mainly in focus:

• Na macie do ćwiczeń... puts the location first
• Jest mało przestrzeni... starts with the existence/amount idea

The original version sounds natural if you want to emphasize where the lack of space is.

Because a mat is thought of as a surface, so Polish uses na = on.

• na macie = on the mat

If you used w, it would suggest being inside something, which does not fit a normal mat.

This is similar to English:

• on the mat, not in the mat

Mało przestrzeni is understandable and correct, but in everyday Polish many speakers would more often say:

• Na macie do ćwiczeń jest mało miejsca.

Here:

• miejsce = place / room / space

In many practical contexts, mało miejsca sounds more idiomatic than mało przestrzeni.

A rough distinction:

• przestrzeń can sound a bit broader or more abstract
• miejsce is often the everyday choice for room/space

So your sentence is fine, but mało miejsca may sound more natural in casual speech.

Because Polish does not have articles like a and the.

So mata can mean:

• a mat
• the mat

The exact meaning depends on context.

Likewise:

• Na macie do ćwiczeń could mean on an exercise mat or on the exercise mat
• mało przestrzeni = little space, without any article

English speakers often look for article equivalents, but Polish normally expresses definiteness through context rather than separate words.

Here are the main forms:

• na = on
• macie → dictionary form: mata = mat
• do = for / for the purpose of
• ćwiczeń → dictionary form: ćwiczenie = exercise
• jest → dictionary form: być = to be
• mało = little / not much
• przestrzeni → dictionary form: przestrzeń = space

This is useful because in Polish many words change form depending on case and grammar, so the word you see in a sentence is often not the dictionary form.

A natural opposite would be:

• Na macie do ćwiczeń jest dużo przestrzeni.
• Na macie do ćwiczeń jest dużo miejsca.

That means:

• There is a lot of space on the exercise mat.

Here dużo works similarly to mało:

• mało przestrzeni = little space
• dużo przestrzeni = a lot of space

And again, in everyday speech, dużo miejsca is often especially common.