Гарантія й гарантійний строк важливі.

Both і and й can mean and in Ukrainian. The choice is often about sound and flow.

Here, Гарантія й гарантійний строк... sounds smoother than Гарантія і гарантійний строк... because й is commonly used between vowels or where it makes pronunciation easier.

A rough guideline:

• і is the basic form
• й is often used to avoid awkward sound combinations

So this is mostly a matter of euphony, not a change in meaning.

Because the subject is actually two things:

• Гарантія
• гарантійний строк

Together they form a compound subject, so the predicate adjective must be plural.

That is why you get:

• важливий = important, masculine singular
• важлива = important, feminine singular
• важливі = important, plural

Since гарантія й гарантійний строк = warranty and warranty period, Ukrainian uses the plural важливі.

They are in the nominative case because they are the subjects of the sentence.

You can tell from the dictionary forms:

• гарантія = nominative singular
• строк = nominative singular
• гарантійний agrees with строк, so it is also nominative singular masculine

The sentence structure is basically:

• Гарантія й гарантійний строк = subject
• важливі = predicate adjective

Because гарантійний is an adjective meaning warranty-related or under warranty and it modifies строк.

So:

• строк = period, term
• гарантійний строк = warranty period / guarantee period

Ukrainian often uses adjectives where English might use a noun-noun combination. In English, warranty period uses warranty like a modifier; in Ukrainian, that idea is usually expressed with an adjective:

• гарантійний строк not
• гарантія строк

That ending shows it is a masculine singular nominative adjective, agreeing with строк, which is a masculine singular noun.

Compare:

• гарантійний строк = masculine singular
• гарантійна умова = feminine singular
• гарантійне обслуговування = neuter singular
• гарантійні умови = plural

So -ий is there because строк is masculine singular.

Ukrainian has no articles like English a or the.

So a noun like гарантія can mean:

• a warranty
• the warranty
• sometimes just warranty in a general sense

The exact interpretation depends on context. In this sentence, English may naturally translate it with the, but Ukrainian does not need any article.

Yes, Ukrainian word order is fairly flexible, though the neutral order here is very natural.

This sentence:

• Гарантія й гарантійний строк важливі.

could also appear as:

• Важливі гарантія й гарантійний строк.

That alternative puts more emphasis on важливі.

Still, the original version is the most straightforward and neutral for a learner.

A helpful stress guide:

• гаранті́я
• гаранті́йний
• стро́к
• важли́ві

A few pronunciation notes:

• Ukrainian г is usually a voiced sound like a softer h, not the hard English g
• й sounds like English y in yes
• ті in гарантія is soft
• и in важливі is not the same as English ee; it is a separate Ukrainian vowel

A rough English-style approximation:

• ha-ran-TI-ya
• ha-ran-TIY-nyy
• strok
• vazh-LY-vi

These are only approximations, but they can help at first.

Often, yes, both can refer to a period or term, but they are not always identical in usage.

• строк often means a fixed period, duration, deadline, or legally defined term
• термін can also mean term/period, but it is broader and can additionally mean technical term in other contexts

In formal, legal, commercial, and warranty language, гарантійний строк is a very standard phrase.

You may also hear гарантійний термін, and in many contexts it means nearly the same thing. But гарантійний строк is especially common in official or product-related wording.

Grammatically, важливі is an adjective in the plural form, but in this kind of sentence it functions as the predicate, so in English it corresponds to are important.

Ukrainian often uses this pattern without a separate word for are in the present tense.

So:

• Гарантія й гарантійний строк важливі.

literally looks like:

• Warranty and warranty period important.

But natural English needs:

• The warranty and the warranty period are important.

This happens because Ukrainian usually omits to be in the present tense.

In Ukrainian, the verb to be is usually not expressed in the present tense.

So where English says:

• X is important
• X and Y are important

Ukrainian often simply says:

• X важливий / важлива / важливе
• X і Y важливі

That means:

• Гарантія важлива. = The warranty is important.
• Гарантія й гарантійний строк важливі. = The warranty and the warranty period are important.

This is one of the most important structural differences from English.