Mit dem Bügeleisen lässt sich die Bluse schnell bügeln, wenn sie noch ein wenig warm ist.

Mit dem Bügeleisen means with the iron.

It comes first because German often puts a time, manner, or tool phrase at the beginning for emphasis or for stylistic variety. The sentence could also be written as:

Die Bluse lässt sich mit dem Bügeleisen schnell bügeln, wenn sie noch ein wenig warm ist.

That would still be correct. Putting Mit dem Bügeleisen first highlights the tool being used.

Because mit always takes the dative case.

• das Bügeleisen = nominative/accusative
• dem Bügeleisen = dative

So:

• mit das Bügeleisen ❌
• mit dem Bügeleisen ✅

Also, Bügeleisen is a neuter noun, so its dative singular article is dem.

This is a very common German structure:

sich lassen + infinitive

It often means something like:

• can be ...
• is easy/possible to ...
• allows itself to be ...

So:

Die Bluse lässt sich schnell bügeln
= The blouse can be ironed quickly
or
= The blouse is easy to iron quickly

It is not about someone actively letting something happen in the usual sense of lassen. It is a special pattern that expresses possibility.

Not in the usual English sense.

In sich lassen + infinitive, sich is part of the construction. You can think of it roughly as:

The blouse lets itself be ironed quickly.

That literal translation sounds unnatural in English, but it helps explain the grammar.

So yes, sich is grammatically reflexive, but the whole phrase functions more like a passive-like expression of possibility.

Because the subject is die Bluse, which is singular.

The finite verb must agree with the subject:

• die Bluse lässt sich bügeln = singular
• die Blusen lassen sich bügeln = plural

So lässt matches die Bluse.

Because lassen is the conjugated verb, and bügeln is an infinitive that goes to the end of the clause.

This is very common in German when one verb is conjugated and another stays in the infinitive:

• Ich will schlafen.
• Das kann man machen.
• Die Bluse lässt sich bügeln.

So in this sentence:

• lässt = finite verb in second position
• bügeln = infinitive at the end of the main clause

Yes, die Bluse is the subject.

Even though the sentence starts with Mit dem Bügeleisen, that first phrase is not the subject. It is just an adverbial phrase.

Main clause structure:

• Mit dem Bügeleisen = prepositional phrase
• lässt = finite verb
• sich die Bluse = subject phrase with the reflexive element
• schnell bügeln = rest of the predicate

A useful point: in German, the subject does not always come first. The finite verb is usually in second position, and something else can stand first.

Schnell is an adverb meaning quickly. In German, adverbs often appear before the infinitive or participle they modify.

So:

die Bluse schnell bügeln = to iron the blouse quickly

That word order is very normal.

You could move adverbs around in some contexts, but schnell bügeln is the most natural phrasing here.

This is a subordinate clause introduced by wenn = when / if.

In subordinate clauses, the conjugated verb goes to the end:

• wenn sie noch ein wenig warm ist

Compare with a main clause:

• Sie ist noch ein wenig warm.

So the subordinate clause word order is completely normal:

• wenn
  • subject + other elements + verb at the end

Sie refers to die Bluse.

That is clear because:

• die Bluse is feminine singular
• sie can mean she/it for a feminine noun

It does not refer to das Bügeleisen, because that noun is neuter, and the pronoun would be es, not sie.

So the meaning is:

when the blouse is still a little warm

It means still a little warm.

Breakdown:

• noch = still
• ein wenig = a little
• warm = warm

So the idea is that ironing works well if the blouse has not completely cooled down yet.

A very natural English equivalent is:

• when it is still slightly warm
• if it is still a little warm

Either can work, depending on context.

In German, wenn can mean:

• when for repeated or general situations
• if for conditions

Here the sentence expresses a practical condition, so English might naturally say:

• if it is still a little warm

But when it is still a little warm also fits if the meaning is more like a general tip.

So both are possible in translation.

It is passive-like, but not a true passive.

A true passive would be:

Die Bluse kann schnell gebügelt werden.
= The blouse can be ironed quickly.

Your sentence uses sich lassen + infinitive, which often sounds a bit more natural or idiomatic in German. It suggests that the blouse is easy or possible to iron in that condition.

So:

• Die Bluse lässt sich schnell bügeln. = idiomatic, common
• Die Bluse kann schnell gebügelt werden. = also correct, more clearly passive

Yes.

• mit dem Bügeleisen = with the iron / with the ironing iron already known or understood
• mit einem Bügeleisen = with an iron / any iron

In many contexts, mit dem Bügeleisen sounds natural because people are thinking of the usual tool for ironing. But mit einem Bügeleisen is also grammatically correct.

Yes, several.

For example:

• Man kann die Bluse schnell bügeln, wenn sie noch ein wenig warm ist.
• Die Bluse kann schnell gebügelt werden, wenn sie noch ein wenig warm ist.
• Wenn die Bluse noch ein wenig warm ist, lässt sie sich schnell bügeln.

These all express roughly the same basic idea, but your original sentence is very natural and idiomatic German.