Om jag hade haft mer tid, skulle jag ha strukit skjortan och sytt fast blixtlåset själv.

Yes. This is a past unreal conditional: it talks about something that did not happen in the past, but could have happened under different circumstances.

The pattern is:

• Om + pluperfect in the if-clause
• skulle ha + supine in the main clause

So:

• Om jag hade haft mer tid = If I had had more time
• skulle jag ha strukit skjortan ... = I would have ironed the shirt ...

This is very close to English:

• If I had had more time, I would have ironed the shirt and sewn on the zipper myself.

Swedish often uses this structure exactly where English uses had had / would have done.

It is strange-looking, but completely normal.

• ha = to have
• hade = past tense of ha
• haft = supine form of ha

So hade haft literally matches English had had.

In this sentence:

• Om jag hade haft mer tid = If I had had more time

This is the normal pluperfect form in Swedish:

• hade + supine

Examples:

• Jag hade sett filmen. = I had seen the film.
• Hon hade kommit hem. = She had come home.
• Vi hade haft pengar. = We had had money.

This is because Swedish has verb-second word order in main clauses.

When the sentence starts with the if-clause:

• Om jag hade haft mer tid, ...

that whole clause takes the first position. Then the finite verb in the main clause must come next:

• ..., skulle jag ha strukit ...

So the order is:

1. fronted element: Om jag hade haft mer tid
2. finite verb: skulle
3. subject: jag

Compare:

• Jag skulle ha strukit skjortan.
• Om jag hade haft mer tid, skulle jag ha strukit skjortan.

Both are correct; the word order changes because the sentence begins differently.

In this sentence, they are best understood as supine forms, because they come after ha.

In Swedish grammar, the supine is used with har, hade, and ha to form compound tenses.

So:

• stryka → strukit
• sy → sytt

Examples:

• Jag har strukit skjortan.
• Jag hade sytt fast blixtlåset.
• Jag skulle ha strukit skjortan.

The past participle is a different form in Swedish and behaves more like an adjective:

• en struken skjorta = an ironed shirt
• ett sytt plagg = a sewn garment

So although English often uses one form for both jobs, Swedish usually distinguishes them more clearly.

Because in Swedish, when two verbs share the same auxiliary, you normally say the auxiliary only once.

So:

• skulle jag ha strukit skjortan och sytt fast blixtlåset själv

means:

• would I have ironed the shirt and sewn the zipper on myself

The second verb sytt is understood to depend on the same ha.

This is completely normal and natural. Repeating ha would usually sound unnecessary.

Compare:

• Jag har tvättat och strukit skjortan.
• Hon hade läst boken och skrivit en recension.

Sy fast is a particle verb. It means to sew something on / attach something by sewing.

So:

• sy = to sew
• sy fast = to sew on / sew firmly in place

In the sentence:

• sytt fast blixtlåset = sewn the zipper on / sewn the zipper into place

Swedish often has verbs like this, where a small word such as fast, upp, på, av, or in changes the meaning.

Examples:

• sätta på = put on / switch on
• ta av = take off
• skriva upp = write down
• sy fast = sew on

The particle often stays separate in many sentence patterns, which is why you see sytt fast rather than a single written word.

Because Swedish uses the definite form here: the zipper, not just a zipper.

• ett blixtlås = a zipper
• blixtlåset = the zipper

The ending -et shows that it is a neuter noun (ett-word) in the singular definite form.

So:

• sytt fast blixtlåset = sewn on the zipper / sewn the zipper into place

This often matches English the.

For the same reason as blixtlåset: it is in the definite form.

• en skjorta = a shirt
• skjortan = the shirt

So:

• strukit skjortan = ironed the shirt

In many contexts, Swedish uses the definite form where English would also use the.

Here själv means myself or personally / on my own.

So:

• ... själv adds the idea that I would have done it myself, without someone else doing it for me.

Placing själv at the end is very natural. It gives emphasis to the idea of doing the actions personally.

So the sentence means something like:

• If I had had more time, I would have ironed the shirt and sewn on the zipper myself.

You can sometimes move själv, but the end position is very common and idiomatic here.

Yes, both are irregular.

stryka = to iron

Common forms:

• infinitive: stryka
• present: stryker
• past: strök
• supine: strukit

Example:

• Jag strök skjortan igår. = I ironed the shirt yesterday.
• Jag har strukit skjortan. = I have ironed the shirt.

sy = to sew

Common forms:

• infinitive: sy
• present: syr
• past: sydde
• supine: sytt

Example:

• Hon sydde fast knappen. = She sewed the button on.
• Hon har sytt en klänning. = She has sewn a dress.

These are worth memorizing, because their forms are not fully predictable.

Not in the same way, and not as the normal choice here.

For a standard past unreal conditional, Swedish normally prefers:

• Om jag hade haft mer tid, skulle jag ha ...

Using skulle in the if-clause can happen in Swedish, but it usually gives a different nuance and is not the standard form for this kind of sentence.

So for a learner, the safest pattern is:

• Om + hade + supine
• skulle + subject + ha + supine

That is exactly what your sentence does.

Yes, in this sentence om means if.

• Om jag hade haft mer tid = If I had had more time

This is the normal word for introducing a condition.

But om can also mean whether in other contexts:

• Jag vet inte om han kommer. = I don't know whether he is coming.

So the meaning depends on context:

• condition → if
• indirect yes/no question → whether

A rough breakdown is:

• Om = if
• jag = I
• hade haft = had had
• mer tid = more time
• skulle jag ha strukit = would I have ironed
• skjortan = the shirt
• och = and
• sytt fast = sewn on / sewn into place
• blixtlåset = the zipper
• själv = myself

A more natural English translation would be:

• If I had had more time, I would have ironed the shirt and sewn on the zipper myself.

So even though the structure is close to English, the main things to notice are:

• the Swedish conditional pattern
• the verb-second word order
• the supine forms
• the particle verb sy fast

It sounds natural and correct. It is a fairly normal written and spoken sentence.

What may feel a bit formal to a learner is not the vocabulary, but the fact that it uses a full past unreal conditional, which is naturally a bit more structured:

• Om jag hade haft mer tid, skulle jag ha ...

But native speakers absolutely use this pattern.

In casual speech, some people may simplify things slightly depending on context, but the sentence you have is standard, idiomatic Swedish.