Лопата й граблі готові.

In Ukrainian, the present-tense form of to be is usually not stated in simple sentences like this.

So:

• Лопата й граблі готові. = The shovel and the rake are ready.

A literal word-for-word version would be closer to:

• Shovel and rake ready.

This is completely normal in Ukrainian. The meaning are is understood automatically.

Й and і both mean and.

In many cases, Ukrainian chooses between them mainly for smooth pronunciation.
Here, й is used after лопата so the phrase flows better:

• Лопата й граблі

If you used і instead, people would still understand you:

• Лопата і граблі

But й often sounds more natural between certain sounds. This is similar to how languages sometimes adjust small words for ease of speaking.

Граблі is one of those Ukrainian nouns that is normally used only in the plural. It means rake or a rake in English, even though English treats it as singular.

So:

• граблі = a rake / rake
• literally, its form is plural

This is why the sentence treats the whole subject as plural.

A similar idea exists in English with words like scissors or pants, which are grammatically plural even when referring to one object.

Готові is the plural form of ready.

The subject is:

• лопата = shovel
• граблі = rake

Together they form a compound subject: the shovel and the rake.
Because there are two things, the adjective must be plural:

• готові = ready (plural)

Compare:

• Лопата готова. = The shovel is ready.
• Граблі готові. = The rake is ready.
• Лопата й граблі готові. = The shovel and the rake are ready.

If the sentence only talked about лопата, then yes, you would use the feminine singular form:

• Лопата готова.

But here the subject is not just лопата. It is:

• лопата й граблі

That means two items together, so the adjective becomes plural:

• готові

So the plural form overrides the singular gender of лопата.

They are in the nominative case, because they are the subject of the sentence.

This is the dictionary/basic form for both words here:

• лопата = nominative singular
• граблі = nominative plural

Since the sentence is simply saying what these things are like (ready), nominative is what you expect for the subject.

Yes. Ukrainian word order is fairly flexible, though the most neutral version here is:

• Лопата й граблі готові.

You could also say:

• Готові лопата й граблі.
• Граблі й лопата готові.

These versions may sound slightly different in emphasis, but the core meaning stays the same.

The original sentence sounds like a straightforward neutral statement.

A rough pronunciation guide is:

• Лопата й граблі готові
• loh-PAH-ta y HRAH-bli hoh-TOH-vee

A few notes:

• г in Ukrainian is usually pronounced like a softer h sound, not a hard English g
• й sounds like English y in yes
• stress is roughly:
  • лопа́та
  • гра́блі
  • гото́ві

Ukrainian has no articles like a or the.

So Лопата й граблі готові can mean:

• The shovel and the rake are ready
• A shovel and a rake are ready
• Shovel and rake are ready

The exact English choice depends on context. In many situations, the shovel and the rake are ready is the most natural translation, but Ukrainian itself does not mark that distinction with articles.