Сіра платіжна картка нова.

In Ukrainian, the present-tense verb бути (to be) is usually omitted in simple sentences like this.

So:

• Сіра платіжна картка нова.

literally looks like:

• Gray payment card new

but naturally means:

• The gray payment card is new
• or A gray payment card is new, depending on context

In the past or future, Ukrainian normally does use a form of бути:

• Сіра платіжна картка була нова. = The gray payment card was new.
• Сіра платіжна картка буде нова. = The gray payment card will be new.

Because they are all agreeing with картка, which is:

• feminine
• singular
• nominative

Ukrainian adjectives must agree with the noun they describe, and predicate adjectives also match the subject.

So:

• сіра = gray, feminine singular
• платіжна = payment, feminine singular
• нова = new, feminine singular

If the noun were masculine, you would get forms like:

• сірий
• платіжний
• новий

It is in the nominative singular.

That is the normal case for the subject of a sentence. The whole subject phrase is:

• сіра платіжна картка = gray payment card

The predicate adjective нова is also in the nominative feminine singular, matching the subject.

Because нова is not just another adjective inside the noun phrase here. It is the predicate adjective: it tells you something about the card.

So the structure is:

• [Сіра платіжна картка] [нова].
• [The gray payment card] [is new].

If you put нова before картка:

• Нова сіра платіжна картка

that normally becomes just a noun phrase meaning:

• a new gray payment card

So the original sentence is a full statement, while нова сіра платіжна картка is usually just the name of an object, not a complete sentence by itself.

Платіжна картка means payment card or bank card.

It is broader than credit card. Depending on context, it could refer to:

• a debit card
• a credit card
• a payment card in general

If you specifically want credit card, Ukrainian often uses:

• кредитна картка

If you specifically want debit card, you may see:

• дебетова картка

Both words describe картка, but they do different jobs:

• сіра gives a visible quality: color
• платіжна gives the type or category of card

In Ukrainian, a more classifying adjective often stands closer to the noun, so:

• сіра платіжна картка

sounds natural: first the descriptive detail, then the more category-like adjective right before the noun.

That said, Ukrainian word order is more flexible than English, and different orders can be used for emphasis.

You do not know from the sentence alone, because Ukrainian has no articles like a or the.

So:

• Сіра платіжна картка нова.

could mean:

• A gray payment card is new
• The gray payment card is new

Context tells you which one is meant.

Yes. Платіжна is an adjective meaning something like payment-related.

It comes from the noun платіж = payment.

So:

• платіжна картка = payment card

This is very common in Ukrainian: a noun can have an adjective built from it and used to classify another noun.

No. In this sentence, no dash is needed.

• Сіра платіжна картка нова.

is perfectly normal.

A dash is more commonly used in some other kinds of verbless sentences, especially when the predicate is a noun, or when the writer wants extra emphasis. With an adjective predicate like нова, leaving out the dash is the standard neutral choice.

Yes, Ukrainian word order is fairly flexible, but changing it often changes the emphasis.

For example:

• Сіра платіжна картка нова.
  Neutral: The gray payment card is new.

• Картка нова.
  Simpler sentence: The card is new.

• Нова сіра платіжна картка
  Usually just a noun phrase: a new gray payment card

So the exact order matters, especially if you want a full sentence rather than just a noun phrase.