Taj predmet mi je zanimljiv, dok je mom bratu matematika draža.

Mi is the unstressed dative form of ja and means to me.

So Taj predmet mi je zanimljiv is literally That subject is interesting to me. Croatian often uses the dative with adjectives that describe how something feels to a person, such as zanimljiv (interesting), dosadan (boring), or drag (dear / liked).

Because they agree with predmet, which is masculine singular nominative.

• taj = masculine singular nominative of that
• zanimljiv = masculine singular nominative of interesting
• predmet = masculine singular noun

In Croatian, demonstratives and adjectives must match the noun in gender, number, and case.

Because bratu is in the dative case, and mom matches it.

The second clause literally means something like mathematics is dearer to my brother. Just as mi means to me, mom bratu means to my brother.

So:

• moj brat = my brother (nominative)
• mom bratu = to my brother (dative)

Draža is the feminine singular form of the comparative adjective draži, from drag.

In this sentence, drag / draži does not mean only dear in an emotional sense. It often means preferred, more appealing, or liked more. So matematika draža means mathematics is preferred / more appealing.

A natural English translation is often my brother prefers mathematics.

Because draža agrees with matematika, which is feminine singular.

• matematika = feminine singular
• therefore the adjective must also be feminine singular: draža

If the noun were masculine, you would use draži instead.

Because matematika is the grammatical subject of the clause.

Croatian often expresses preference with drag / draži plus a dative experiencer:

• Matematika je mom bratu draža.
• literally: Mathematics is dearer to my brother.

This is different from a verb like voljeti:

• Moj brat više voli matematiku.
• here matematiku is accusative because it is the object of voli.

Here dok means whereas or while in a contrastive sense.

It is not mainly about two actions happening at the same time. It connects two ideas that are being contrasted:

• That subject is interesting to me
• whereas my brother prefers mathematics

So in this sentence, dok is best understood as a contrast marker.

Croatian word order is flexible, but short unstressed words like mi and je tend to appear near the beginning of the clause.

So:

• mi je = to me is
• dok je mom bratu... = after dok, the clitic je comes very early in the clause

This is normal Croatian clitic placement. English speakers often want a more fixed English-style order, but Croatian does not work that way.

Yes.

• mi and meni both mean to me
• mom bratu and mojem bratu both mean to my brother

The shorter forms (mi, mom) are very common and natural. The longer forms can sound more emphatic, more careful, or simply a bit fuller depending on context.

For example:

• Taj predmet meni je zanimljiv can sound more contrastive: That subject is interesting to me
• mojem bratu is a perfectly normal alternative to mom bratu

Because Croatian can leave the comparison implicit when the context is clear.

Here the sentence sets up a contrast between that subject and mathematics, so draža naturally suggests dearer / preferred than that subject.

If you wanted to say it explicitly, you could say:

• Matematika je mom bratu draža od tog predmeta.

But in the original sentence, that extra part is not necessary.