Diese Bluse lässt sich leicht bügeln.

Because Bluse is a feminine noun and here it is the subject of the sentence, so it is in the nominative case.

• die Bluse = the blouse
• diese Bluse = this blouse

If it were in a different case, the form of dies- could change:

• nominative: diese Bluse
• accusative: diese Bluse
• dative: dieser Bluse
• genitive: dieser Bluse

So in this sentence, diese is correct because the blouse is the thing being talked about as the subject.

In this sentence, lässt sich + infinitive means something like:

• can be ...
• is easy/possible to ...
• can be done ...

So:

• Diese Bluse lässt sich leicht bügeln.
  = This blouse can be ironed easily.
  = This blouse is easy to iron.

This is a very common German structure. It often describes what is possible with something.

Some similar examples:

• Das Fenster lässt sich leicht öffnen.
  = The window can be opened easily.
• Der Text lässt sich gut lesen.
  = The text is easy to read.

Grammatically, yes, it uses the reflexive pronoun sich, but in this pattern it does not mean that the blouse is literally doing something to itself.

In sich lassen + infinitive, sich is part of a fixed construction that expresses possibility or manageability.

So you should learn sich lassen + infinitive as a set phrase:

• Das Problem lässt sich lösen.
  = The problem can be solved.
• Die Tür lässt sich nicht schließen.
  = The door cannot be closed.

Even though sich is there, the meaning is often close to a passive idea in English.

Because this sentence has a verb combination:

• the finite verb: lässt
• the infinitive: bügeln

In German main clauses, the finite verb goes in second position, and the infinitive usually goes to the end.

So the structure is:

• Diese Bluse = subject
• lässt = finite verb in position 2
• sich leicht = middle part
• bügeln = infinitive at the end

This is very normal in German:

• Er will heute arbeiten.
• Das Auto lässt sich gut fahren.

They are similar, but leicht is the more natural choice here.

• leicht often means easily
• einfach often means simple, easy, or simply

In the sentence Diese Bluse lässt sich leicht bügeln, leicht sounds very idiomatic because it describes how easily the action can be done.

You may also hear:

• Diese Bluse ist leicht zu bügeln.
• Diese Bluse lässt sich einfach bügeln.

But lässt sich leicht bügeln is especially natural.

Yes. That is grammatically correct and means almost the same thing:

• Diese Bluse kann leicht gebügelt werden.
  = This blouse can be ironed easily.

But the two versions feel a little different:

• lässt sich leicht bügeln sounds more natural and idiomatic in everyday German
• kann ... gebügelt werden is a more straightforward passive construction and can sound a bit more formal or heavier

So both are correct, but native speakers often prefer lässt sich in this kind of sentence.

That is one of the meanings of lassen, but lassen has several uses in German.

A few common ones are:

• to let / allow
  
  • Lass mich gehen. = Let me go.
• to have something done
  
  • Ich lasse meine Haare schneiden. = I have my hair cut.
• to leave something
  
  • Ich lasse das Buch hier. = I leave the book here.
• in the pattern sich lassen + infinitive = can be / is possible to

So in your sentence, lassen does not mean let in the simple English sense. It belongs to the special pattern sich lassen + infinitive.

It is not a normal passive sentence, but it often has a passive-like meaning.

Compare:

• Diese Bluse lässt sich leicht bügeln.
  = This blouse can be ironed easily. / This blouse is easy to iron.
• Diese Bluse wird leicht gebügelt.
  = This blouse is being ironed easily / is ironed easily.
• Diese Bluse kann leicht gebügelt werden.
  = This blouse can be ironed easily.

So lässt sich + infinitive is often called a kind of middle-style construction because it is active in form but passive in meaning.

Yes, absolutely.

• Diese Bluse lässt sich leicht bügeln.
• Diese Bluse ist leicht zu bügeln.

Both mean roughly the same thing: This blouse is easy to iron.

The difference is mainly stylistic:

• ist leicht zu bügeln directly describes the blouse as easy to iron
• lässt sich leicht bügeln emphasizes that ironing it is readily possible / manageable

Both are common and natural.

Because leicht is functioning as an adverb here, modifying the action bügeln.

It tells you how the blouse can be ironed:

• leicht bügeln = iron easily

German adverbs are often placed before the infinitive or participle they relate to:

• gut lesen
• schwer verstehen
• leicht öffnen

So leicht comes before bügeln because it describes the manner of ironing.

Yes:

• Diese Bluse lässt sich bügeln.

This means:

• This blouse can be ironed.

That is grammatical, but it says less. It only tells you that ironing the blouse is possible. Adding leicht makes the meaning more useful and natural:

• Diese Bluse lässt sich leicht bügeln.
  = This blouse is easy to iron.

Without leicht, the sentence may sound a bit more neutral or context-dependent.