A macska maradhat, feltéve, hogy tiszta a macskaalom.

Maradhat comes from the verb marad = to stay / remain.

The ending -hat / -het adds the idea of can / may / be allowed to.

So:

• marad = stays / will stay
• maradhat = can stay / may stay

In this sentence, A macska maradhat means something like The cat can stay or The cat may stay.

Hungarian has two forms of the definite article:

• a before a consonant sound
• az before a vowel sound

Since macska starts with m, you use a:

• a macska = the cat

This is similar to English a/an, but note that a/az means the, not a/an.

Yes. Feltéve, hogy is best learned as a fixed expression meaning:

• provided that
• on condition that
• assuming that

It introduces a condition.

So:

• A macska maradhat, feltéve, hogy...
  = The cat may stay, provided that...

This expression is a bit more formal than everyday ha = if.

Yes.

A more everyday version would be:

• A macska maradhat, ha tiszta a macskaalom.

That also means The cat can stay if the litter is clean.

The difference is mostly in style:

• ha = normal, everyday if
• feltéve, hogy = more formal, more like provided that

In Hungarian, the verb to be is often omitted in the present tense when the predicate is a noun or adjective in the 3rd person.

So Hungarian says:

• A macskaalom tiszta.
• Tiszta a macskaalom.

Both mean:

• The litter is clean.

There is no separate word for is here.

This is a very common Hungarian pattern.

Both are grammatical, but they are not exactly identical in emphasis.

• A macskaalom tiszta. = more neutral: The litter is clean.
• Tiszta a macskaalom. = puts more attention on clean

Hungarian word order is flexible and often shows focus or emphasis, not just basic grammar.

In this sentence, tiszta comes first because the cleanliness is the important condition.

Macskaalom is a compound noun:

• macska = cat
• alom = litter / bedding

Together, macskaalom means cat litter, and depending on context it can also refer to the litter setup or litter box area.

Hungarian very often forms compound nouns by joining words together with no space.

It can mean either, depending on context.

The -hat / -het ending can express:

• possibility
• ability
• permission

In this sentence, because a condition is being given, English often understands it as permission:

• The cat may stay, provided that...

But can stay is also a perfectly natural translation.

Yes.

You can say:

• Feltéve, hogy tiszta a macskaalom, a macska maradhat.

That means the same thing, but it sounds quite formal.

A more natural everyday version with the condition first would be:

• Ha tiszta a macskaalom, a macska maradhat.

So the order is flexible.

Because feltéve, hogy is written as a conjunction-like expression with a comma before hogy.

So this is standard:

• feltéve, hogy

Also, Hungarian normally separates subordinate clauses with commas, so the punctuation in the full sentence is completely normal:

• A macska maradhat, feltéve, hogy tiszta a macskaalom.

If you use ha, there is no internal comma inside the expression, just the clause-separating comma:

• A macska maradhat, ha tiszta a macskaalom.