Die Verkäuferin in der Gärtnerei sagt, unser Strauch habe den Winter gut überstanden.

Because this sentence uses indirect speech (reported speech). After a verb like sagt, German often uses Konjunktiv I to show that this is what someone says, not necessarily what the speaker is directly confirming.

So:

• direct statement: Unser Strauch hat den Winter gut überstanden.
• reported version: Die Verkäuferin sagt, unser Strauch habe den Winter gut überstanden.

Here, habe is the Konjunktiv I form of haben for er/sie/es.

Yes, especially in written German or more formal styles. Konjunktiv I is the standard grammar for reported speech.

In everyday spoken German, many people would more naturally say:

• Die Verkäuferin sagt, dass unser Strauch den Winter gut überstanden hat.

or even:

• Die Verkäuferin sagt, unser Strauch hat den Winter gut überstanden.

So the sentence you have is grammatically normal, but it sounds a bit more formal or written.

German can report speech in two common ways:

1. with dass

   • Die Verkäuferin sagt, dass unser Strauch den Winter gut überstanden habe/hat.

2. without dass

   • Die Verkäuferin sagt, unser Strauch habe den Winter gut überstanden.

When dass is omitted, this kind of reported clause often keeps main-clause word order, so the verb comes early: unser Strauch habe...

Because this is not a dass-clause here. If you had dass, the verb would go to the end:

• ..., dass unser Strauch den Winter gut überstanden habe.

But in the actual sentence, dass is omitted, so the clause uses verb-second order:

• ..., unser Strauch habe den Winter gut überstanden.

That is why habe comes right after unser Strauch.

Because sagt is followed by another clause: the content of what the saleswoman says.

German normally uses a comma before this kind of clause, whether it begins with dass or whether dass is omitted.

So:

• Die Verkäuferin sagt, dass ...
• Die Verkäuferin sagt, unser Strauch habe ...

Both need the comma.

Gärtnerei usually means a plant nursery, garden center, or a business where plants are grown and sold. It is not just a regular garden.

So:

• der Garten = garden
• die Gärtnerei = nursery / garden shop / horticultural business

In this sentence, die Verkäuferin in der Gärtnerei means the saleswoman or shop assistant who works there.

Because this is about location, not movement.

• in der Gärtnerei = in the nursery / at the garden center
• in die Gärtnerei would mean into the nursery

German uses:

• dative after in for location
• accusative after in for direction/movement

Here the saleswoman is located there, so der Gärtnerei is dative.

Because unser Strauch is the subject of the reported clause, so it is in the nominative case.

• unser Strauch = nominative masculine
• unseren Strauch = accusative masculine

You would use unseren Strauch if it were the direct object, but here the shrub is the thing that has survived, so it is the subject.

Because den Winter is the accusative object of überstehen.

The verb überstehen means something like:

• to survive
• to get through
• to come through

So the structure is:

• jemand/etwas übersteht etwas
• the shrub survives the winter

That is why Winter is in the accusative: den Winter.

Überstanden is the past participle of überstehen, which here means to survive or to come through successfully.

Examples of the idea:

• den Winter überstehen = survive the winter
• eine Krankheit überstehen = get through an illness

There is no ge- because this über- verb is inseparable in this meaning. That is why the participle is:

• überstanden, not geüberstanden and not übergestanden

This is something learners often just have to memorize with the verb.

Gut means well, and it adds the idea that the shrub did not just barely survive, but came through the winter in good condition.

So:

• den Winter überstehen = survive the winter
• den Winter gut überstehen = survive the winter well / come through the winter well

It sounds natural in German because people often talk this way about plants, health, or difficult periods.

Yes. Die Verkäuferin is specifically female.

The masculine form is:

• der Verkäufer

In many contexts, a more natural English translation might be sales assistant, shop assistant, or clerk, depending on the shop. So even though the literal meaning is saleswoman, the best English wording can vary by context.

A direct version would be:

• Die Verkäuferin sagt: Unser Strauch hat den Winter gut überstanden.

Or, if you just want the statement itself:

• Unser Strauch hat den Winter gut überstanden.

The main change in reported speech is usually:

• hat → habe

That change signals that the speaker is reporting what the saleswoman says.