Moj uvod je predug, pa ću ga napisati što kraće.

Yes. Both are possible.

In Croatian, short forms like je often like to stand near the beginning of the clause, so Moj je uvod predug can sound a bit more typical in careful standard usage. But Moj uvod je predug is also very common and natural.

The meaning does not really change: both mean that the intro is too long.

Moj means my.

It is a possessive adjective, and it has to agree with the noun it describes. The noun uvod is masculine singular, so the correct form is moj.

Compare:

• moj uvod = my intro
• moja knjiga = my book
• moje pismo = my letter

So the form changes according to the gender and number of the noun.

Predug means too long.

It is built from:

• pre- = too, overly
• dug = long

Croatian very often forms words like this as a single adjective:

• predug = too long
• prekratak = too short
• preskup = too expensive
• prevelik = too big

You can also sometimes express the same idea with previše plus an adjective, but predug is the compact, natural form here.

Here pa means something like so, and so, or therefore.

It connects the two ideas:

• My intro is too long
• so I’ll write it more briefly / as briefly as possible

It is a very common conversational connector in Croatian, and it often sounds more natural than a heavier logical word like zato in sentences like this.

Because Croatian often leaves out subject pronouns when they are already clear from the verb form.

Here ću already shows first person singular future, so the listener understands that the subject is I.

So:

• pa ću ga napisati... = normal, natural
• pa ja ću ga napisati... = possible, but it adds emphasis or contrast

Croatian does not need to state ja as often as English needs I.

Ću is a short auxiliary form, called a clitic. In Croatian, clitics usually appear very near the beginning of the clause.

So in:

• pa ću ga napisati

the auxiliary comes early, which is exactly what you expect.

This early placement is normal for short forms such as:

• sam
• si
• je
• ću
• se

You usually cannot move them around as freely as full words in English.

Because Croatian clitics have a fairly fixed order.

Both ću and ga are short clitic forms:

• ću = auxiliary for the future
• ga = him/it as a short object pronoun

When they appear together, the auxiliary normally comes before the object pronoun:

• ću ga

So:

• pa ću ga napisati = correct, natural
• pa ga ću napisati = not natural in standard Croatian

Ga refers back to uvod.

So it means it here:

• napisati ga = write it

Grammatically, ga is the accusative singular clitic pronoun here, because it is the direct object of napisati.

English uses it without grammatical gender, but Croatian pronouns reflect the gender of the noun they refer to. Since uvod is masculine, the pronoun is ga.

Because napisati is perfective, while pisati is imperfective.

Very roughly:

• pisati = to write, to be writing, to write in general
• napisati = to write and complete, to finish writing

In this sentence, the speaker means a single completed action: they will produce a finished version of the intro. That is why napisati fits well.

So:

• napisat ću ga... / ću ga napisati... = I will write it, finish writing it
• pisat ću ga... can sound more like focusing on the process or activity

Here što is not really functioning as the question word what.

The pattern što + comparative means as ... as possible.

So:

• što kraće = as briefly as possible / as short as possible
• što brže = as quickly as possible
• što bolje = as well as possible

A fuller version would be:

• što je moguće kraće = as short as possible

In everyday language, the shorter form što kraće is very common.

Because here the word is functioning adverbially: it describes how the person will write the intro.

Compare:

• kraći uvod = a shorter intro
  Here kraći is an adjective describing the noun uvod.
• napisati ga kraće = write it more briefly / more shortly
  Here kraće modifies the verb.

So in što kraće, the idea is:

• write it more briefly
• or, more naturally in English, as briefly as possible

This is why kraće is the correct form in this sentence.