Meine Mutter sagt, Blumenkohl und Zucchini seien im Sommer besonders frisch.

Seien is the Konjunktiv I form of sein for they. German often uses Konjunktiv I for indirect speech: it shows that the speaker is reporting someone else’s statement.

So this sentence means something like: My mother says that cauliflower and zucchini are especially fresh in summer, but the German makes it clearer that this is her statement being reported.

Compare:

Direct statement:
Blumenkohl und Zucchini sind im Sommer besonders frisch.

Reported speech:
Meine Mutter sagt, Blumenkohl und Zucchini seien im Sommer besonders frisch.

No. It is not required in everyday German.

You could also say:

Meine Mutter sagt, Blumenkohl und Zucchini sind im Sommer besonders frisch.

or

Meine Mutter sagt, dass Blumenkohl und Zucchini im Sommer besonders frisch sind.

Using seien sounds more like formal reporting, written German, journalism, or careful style. In normal conversation, many speakers would simply use sind.

German can report speech without dass.

So both of these are possible:

Meine Mutter sagt, Blumenkohl und Zucchini seien im Sommer besonders frisch.

Meine Mutter sagt, dass Blumenkohl und Zucchini im Sommer besonders frisch seien.

The version without dass is perfectly normal. One important difference is word order:

• without dass: Blumenkohl und Zucchini seien ...
• with dass: ..., dass Blumenkohl und Zucchini ... seien

With dass, the finite verb goes to the end of the clause.

Because they are being used generically, meaning vegetables in general, not specific individual items.

This is similar to English:

Cauliflower and zucchini are especially fresh in summer.

You are talking about those foods as types of food, so German often leaves out the article.

If you meant specific ones, you would usually add articles or other determiners, for example:

Der Blumenkohl und die Zucchini im Kühlschrank sind noch frisch.

It can be a little confusing because Zucchini is often the same in singular and plural.

• singular: die Zucchini
• plural: die Zucchini

In this sentence, it is best understood as a generic noun: zucchini as a type of vegetable.

Also, the verb is plural anyway because the subject is Blumenkohl und Zucchini joined by und. Two coordinated nouns make a plural subject, so the verb is seien.

Im is a contraction of in dem.

Since Sommer is masculine (der Sommer), in dem Sommer becomes im Sommer.

So:

• der Sommer
• in dem Sommer
• im Sommer

This is the normal way to say in summer in German.

Here frisch is a predicate adjective with sein, and besonders modifies frisch.

So besonders frisch works as a unit meaning especially fresh.

German often places this kind of information toward the end of the clause:

... seien im Sommer besonders frisch.

That sounds very natural.

Other word orders are possible, but they change the emphasis a bit. For example:

... seien besonders im Sommer frisch.

This puts more focus on especially in summer.

Because German uses a comma to separate the main clause from the following reported clause.

Main clause:
Meine Mutter sagt

Reported clause:
Blumenkohl und Zucchini seien im Sommer besonders frisch

German punctuation is stricter than English here, so the comma is required.

Because seien is Konjunktiv I, which is the usual form for reported speech.

Wären is Konjunktiv II, which is more often used for things like:

• hypotheticals
• unreal situations
• politeness
• or as a substitute when Konjunktiv I looks identical to the normal indicative form

Since seien is a clear and distinct Konjunktiv I form, it is the natural choice here.

So:

• seien = reported speech
• wären = would be / were, more hypothetical or unreal

Yes. A very common alternative is:

Meine Mutter sagt, dass Blumenkohl und Zucchini im Sommer besonders frisch sind.

This is probably the version many learners will hear most often in everyday life.

The difference is mainly one of style:

• seien = more formal, more explicitly reported
• sind = more neutral, everyday, conversational

Both can be correct depending on context.