Door de griep bleef zij thuis.

Here door means because of or due to, not through.

So door de griep means because of the flu. Dutch often uses door to introduce a cause, especially when something is caused by an outside factor and often by something negative or unwanted.

Examples:

• Door de regen kwamen we te laat.
• Door een fout werkte het niet.

So in this sentence, de griep is the reason she stayed home.

That is because Dutch main clauses follow the verb-second rule.

In a normal statement, the finite verb comes in the second position:

• Zij bleef thuis.

If you put another element first, such as Door de griep, the verb still has to stay second:

• Door de griep bleef zij thuis.

So the order is:

1. Door de griep
2. bleef
3. zij
4. thuis

This is called inversion: the subject comes after the finite verb because something else was moved to the front.

Bleef is the simple past singular of blijven (to stay, to remain).

Forms of blijven:

• present: ik blijf, zij blijft
• past singular: ik bleef, zij bleef
• past plural: wij bleven
• past participle: gebleven

So bleef zij thuis means she stayed home.

This is an irregular verb, so you just have to learn the past form.

Both are possible.

• zij is the full form
• ze is the unstressed short form

In everyday Dutch, ze is very common:

• Door de griep bleef ze thuis.

Zij can sound a bit more formal, clearer, or slightly more emphatic. In many contexts, the difference is small, but learners should know that ze is often what you will hear in speech.

Thuis is an adverb meaning at home or home in the sense of location.

So:

• thuis blijven = stay home
• thuis zijn = be at home

Huis is a noun meaning house.

Compare:

• Ze is thuis. = She is at home.
• Ze is in het huis. = She is in the house.

Dutch usually uses thuis when talking about being at home as a general place, not the physical building.

Dutch very often uses the definite article with griep when referring to the illness someone has.

Common expressions:

• de griep hebben = to have the flu
• door de griep = because of the flu

So de griep is the normal choice here. Using griep without the article is possible in some broader or more abstract contexts, but in this sentence de griep sounds most natural.

Yes. A few natural alternatives are:

• Vanwege de griep bleef ze thuis.
  This also means because of the flu.

• Omdat ze griep had, bleef ze thuis.
  This means Because she had the flu, she stayed home.

• Ze bleef thuis door de griep.
  Grammatically possible, though Door de griep bleef ze thuis is often more natural if you want to emphasize the reason first.

Each version is slightly different in style, but they all express the same basic idea.

Yes, it is natural and correct.

It sounds a bit more written or narrative than the very everyday version:

• Door de griep bleef ze thuis.

The structure is completely normal, and starting with Door de griep is a common way to emphasize the cause.