Learn Hardcore Dutch: Ondanks haar eenvoudige spijkerbroek ziet zij er heel stijlvol uit. - Despite her simple jeans she looks very stylish.

The first position is taken by the prepositional phrase Ondanks haar eenvoudige spijkerbroek, so the verb comes next, and the subject moves after the verb:

Neutral order: Zij ziet er heel stijlvol uit.
With the phrase moved to the front: Ondanks haar eenvoudige spijkerbroek ziet zij er heel stijlvol uit.

So the change is because something other than the subject was placed first.

What exactly does ondanks mean, and how is it used?

Ondanks means despite or in spite of.

It is a preposition and is followed by a noun phrase:

Ondanks de regen – Despite the rain
Ondanks haar eenvoudige spijkerbroek – Despite her simple pair of jeans

It does not change the verb to the end (that would be a conjunction like omdat, terwijl, etc.). Here, the whole phrase Ondanks haar eenvoudige spijkerbroek is just put at the beginning of the sentence, which then triggers the usual V2 word order (ziet second).

Why is it eenvoudige spijkerbroek and not eenvoudig spijkerbroek?

In Dutch, adjectives often get an -e ending before a noun. In this sentence:

spijkerbroek is a de-word (de spijkerbroek)
It has a determiner (haar) before it

With a de-word and a determiner, the adjective takes -e:

haar eenvoudige spijkerbroek – her simple jeans
de lange broek – the long trousers
mijn oude jas – my old coat

You would normally see the form eenvoudig (without -e) in the predicate position, for example:

De spijkerbroek is eenvoudig. – The jeans are simple.

What exactly is a spijkerbroek, and how is it different from broek?

broek = trousers / pants (general word for any kind of trousers)
spijkerbroek = specifically jeans (denim trousers)

Literally, spijkerbroek is something like “nail trousers,” but in modern usage it simply means jeans. So:

een broek – trousers in general
een spijkerbroek – a pair of jeans

Why is zij used instead of ze here? Is there a difference?

Zij and ze both mean she (or they, depending on context). The difference is:

zij: stressed or slightly more emphatic / formal
ze: unstressed, more neutral / colloquial

In this sentence, zij can lightly emphasize the subject:

Ondanks haar eenvoudige spijkerbroek ziet zij er heel stijlvol uit.
→ She looks very stylish (even though you might not expect it).

You could also say:

Ondanks haar eenvoudige spijkerbroek ziet ze er heel stijlvol uit.

Both are correct; ze sounds a bit more casual.

What is the function of er in ziet zij er heel stijlvol uit?

Here er is a kind of dummy / placeholder pronoun that is required by the verb phrase er … uitzien.

The verb er … uitzien means to look (a certain way):

Je ziet er goed uit. – You look good.
Hij ziet er moe uit. – He looks tired.
Zij ziet er heel stijlvol uit. – She looks very stylish.

You cannot simply say Zij ziet heel stijlvol uit; er is part of the standard construction and must be there.

How does the verb er … uitzien work, and why is uit at the end?

Uitzien is a separable verb:

Base verb: uitzien
Separable prefix: uit

In main clauses, the prefix normally goes to the end of the clause, while the finite verb stays in the V2 position. Because er belongs with the verb phrase, it also appears around the verb:

Zij ziet er stijlvol uit. – She looks stylish.
Ondanks haar eenvoudige spijkerbroek ziet zij er heel stijlvol uit.

In other tenses:

Zij heeft er altijd stijlvol uitgezien. – She has always looked stylish.
(Here, uit attaches to the past participle gezien → uitgezien.)

So: in simple main clauses, you get ziet … uit with er in between; in perfect tenses, uit sticks to gezien.

What is the difference between heel stijlvol and words like erg stijlvol or zeer stijlvol?

They all mean roughly very stylish, but with slightly different flavor:

heel stijlvol – very / really stylish (neutral, very common in speech)
erg stijlvol – also very stylish; erg originally means “bad,” but in modern usage it’s a common intensifier, similar to very / really
zeer stijlvol – very stylish, but sounds more formal / written

Note: heel can also mean whole / entire in other contexts (de hele dag – the whole day), but before adjectives like this (heel mooi, heel stijlvol), it usually means very.

Could you say Ondanks haar eenvoudige spijkerbroek is zij heel stijlvol? Is that correct?

Grammatically, yes, it is correct:

Ondanks haar eenvoudige spijkerbroek is zij heel stijlvol.

However, the meaning shifts slightly:

ziet zij er heel stijlvol uit – focuses on her appearance (“she looks stylish”).
is zij heel stijlvol – suggests she is stylish as a general characteristic (style, taste, personality), not just visually in that moment.

In most contexts describing how someone looks, er … uitzien is the more natural choice.

Why does ondanks haar eenvoudige spijkerbroek come at the beginning? Could it go elsewhere?

Yes, that phrase can move. It is put at the beginning to emphasize the contrast (“despite her simple jeans…”). Other possible positions:

Zij ziet er heel stijlvol uit, ondanks haar eenvoudige spijkerbroek.
(More neutral, contrast comes at the end.)
Zij ziet, ondanks haar eenvoudige spijkerbroek, er heel stijlvol uit.
(Possible, but the split feels a bit clumsy in everyday speech.)

Putting it right at the start makes the “despite” part prominent, and then causes the verb to move into second position (ziet).