Кабачок і капуста лежать на прилавку.

Because the subject is made up of two nouns joined by і: кабачок і капуста. In Ukrainian, a compound subject like that normally takes a plural verb.

• кабачок лежить = the zucchini is lying
• капуста лежить = the cabbage is lying
• кабачок і капуста лежать = the zucchini and the cabbage are lying

So лежать agrees with both things together.

They are in the nominative case, because they are the subject of the sentence: they are the things doing the action of лежать.

Dictionary forms:

• кабачок = nominative singular
• капуста = nominative singular

Because на can mean either:

• onto / to a surface, with accusative
• on a surface, with locative

Here the meaning is location, not movement. The vegetables are already there, so Ukrainian uses на + locative:

• на прилавку = on the counter / on the stall
• на прилавок would suggest movement onto the counter

It is the locative singular form of прилавок.

• nominative: прилавок
• locative: на прилавку

After на in the meaning of location, the locative is very common.

Yes. Лежати / лежать literally means to lie or to be lying. It is very natural for objects that are resting somewhere, especially horizontally or simply placed somewhere.

So in Ukrainian, using лежать for vegetables on a counter sounds normal. In English, we might just say are on the counter, but Ukrainian often uses a more physical verb like лежать.

No. Лежать already means are lying.

Ukrainian verbs carry person and number, so you do not need a separate present-tense verb are the way English does here.

So:

• лежать = they lie / they are lying

Yes. Ukrainian word order is fairly flexible.

This sentence could also be:

• На прилавку лежать кабачок і капуста.

That still means the same thing. The difference is mostly emphasis:

• Кабачок і капуста лежать на прилавку focuses first on the vegetables
• На прилавку лежать кабачок і капуста focuses first on the location

Yes, та could also mean and here.

• і = and
• та = and

Both are common. Often the choice is about style or sound. І is the most basic, neutral choice, so it fits perfectly here.

• кабачок is masculine
• капуста is feminine

Their genders matter for things like adjectives or past-tense verbs, but in this sentence the verb is plural, so the important thing is plural agreement, not gender agreement.

For example:

• зелений кабачок
• свіжа капуста

But together:

• кабачок і капуста лежать

Because Ukrainian has no articles.

So Кабачок і капуста лежать на прилавку can mean:

• A zucchini and a cabbage are lying on the counter
• The zucchini and the cabbage are lying on the counter

The exact interpretation depends on context.

A good stress guide is:

• кабачо́к
• і
• капу́ста
• лежа́ть
• на
• прила́вку

A rough pronunciation guide for an English speaker:

kabachOK i kapOOSTa leZHAT na prylAVku

A small note:

• the soft sign in лежать softens the final т
• г does not appear in this sentence, so there is no special issue with that sound here

Yes. Then кабачок would become plural:

• Кабачки і капуста лежать на прилавку.

The verb would still be лежать, because the subject is plural.

So the singular кабачок here tells you it is one zucchini, not several.