Håret bliver kortere, når jeg får det klippet.

Danish often uses the definite form for body parts when it is obvious whose body part is meant. So håret literally means the hair, but in context it naturally means my hair.

So:

• Håret bliver kortere = literally The hair becomes shorter
• natural English = My hair gets shorter

You can say mit hår in some contexts, but håret is very natural here.

It is the definite ending. Danish usually puts the at the end of the noun:

• et hår = a hair / hair
• håret = the hair

Because hår is a neuter noun, its definite ending is -et.

Because bliver means becomes / gets, while er means is.

So:

• Håret er kortere = The hair is shorter
• Håret bliver kortere = The hair becomes / gets shorter

Here the idea is a change: the hair was longer before, and after being cut, it gets shorter.

Kortere is the comparative form of kort:

• kort = short
• kortere = shorter

A lot of Danish adjectives form the comparative with -ere, just like English often adds -er:

• lang → længere = long → longer
• kort → kortere = short → shorter

So Håret bliver kortere means The hair gets shorter.

Here når means when, and often has the sense of whenever in a general situation.

So the sentence means something like:

• My hair gets shorter when/whenever I have it cut

This is different from:

• hvis = if
• da = when for a specific past event

So når is the natural choice here because it describes something that normally happens.

Literally, it means I get it cut or I have it cut.

This is a very common Danish pattern:

• få + object + past participle

It means that you arrange for something to be done, not necessarily that you do it yourself.

For example:

• Jeg får bilen repareret = I get the car repaired
• Jeg får håret klippet = I get my hair cut

So jeg får det klippet does not mean I cut it myself. It means someone cuts it for me, or I have it done.

Because hår is a neuter noun:

• et hår

When Danish uses a pronoun to refer back to a neuter noun, it uses det:

• håret → det

If the noun were a common-gender noun (en word), Danish would usually use den instead.

So det here refers back to håret.

Because klippet is the past participle of klippe.

In the pattern få + object + past participle, Danish uses the past participle:

• klippe = to cut
• klipper = cut / is cutting
• klippet = cut (past participle)

So:

• jeg får det klippet = I get it cut

This is similar to English have/get something done.

Usually it sounds like a general statement:

• My hair gets shorter whenever I have it cut

Because of når, it describes what normally happens in that situation.

But depending on context, it can also refer to a specific future or expected situation:

• My hair gets shorter when I get it cut

So the exact meaning depends a little on context, but the sentence naturally sounds general.

Yes. Those are also natural ways to say it.

For example:

• Jeg får håret klippet
• Jeg får klippet håret
• jeg får det klippet

All can mean I get my hair cut.

In your sentence, det is used because håret was already mentioned in the first clause, so Danish avoids repeating the noun. That makes the sentence flow naturally:

• Håret bliver kortere, når jeg får det klippet.