Learn Hardcore Croatian: Nadam se da će ti se svidjeti ovaj roman.

In Croatian, the verb nadati se (to hope) is inherently reflexive, so it normally appears with se: Nadam se... = I hope...
The se here doesn’t mean myself in a literal sense; it’s simply part of how the verb is used (like a fixed reflexive verb). You generally can’t drop it: Nadam da... is not standard.

Why is there da after Nadam se?

Croatian commonly uses da to introduce a subordinate clause after verbs like nadam se (I hope), mislim (I think), znam (I know), etc.
So Nadam se da... corresponds to I hope that....

What does će mean here, and why is it used?

Će is the future-tense auxiliary for he/she/it/they will (and with clitics it often looks the same across persons).
Here it forms the future: da će ... svidjeti = that ... will like / will be pleasing.

Why is the verb svidjeti se used instead of a direct “to like” verb?

Croatian often expresses “to like” as to be pleasing to someone.
So svidjeti se literally works like: X is pleasing to Y.
That’s why the person who “likes” something is not the grammatical subject.

Why is it ti (dative) and not tebe (accusative) or tvoj (possessive)?

Because with svidjeti se, the “liker” is expressed in the dative case:

svidjeti se meni = to be pleasing to me
svidjeti se tebi / ti = to be pleasing to you

Ti is the short (clitic) dative form of tebi. Tebe is accusative and would be used with different verb patterns (not with svidjeti se).

Why is se placed before svidjeti (and why is the order će ti se svidjeti)?

Će, ti, and se are clitics (unstressed “short” words) that tend to cluster in the second position of the clause (or right after da here).
So after da you often get a clitic cluster like: će + (dative) + se → da će ti se...
The full verb svidjeti comes after that: da će ti se svidjeti...

Why is it ovaj roman and not ovaj romanu or something else?

In this structure, ovaj roman is the thing that will be liked (the thing that is pleasing), so it functions as the grammatical subject of svidjeti se. Subjects are in the nominative case, hence:

ovaj roman (nominative)
Not romanu (dative) or romanom (instrumental), etc.

How do I know ovaj is the correct form of “this”?

Ovaj agrees with the noun in gender, number, and case.

roman is masculine, singular, nominative
So you use ovaj (masc sg nom).
(For comparison: ova knjiga = this book (fem), ovo pismo = this letter (neut).)

Is svidjeti here an infinitive? Why is it not conjugated?

Yes, svidjeti is the infinitive. In the future tense, Croatian typically uses ću/ćeš/će... + infinitive:

(ja) ću doći = I will come
(on) će doći = he will come
So će ... svidjeti is normal: will like / will be pleasing.

Could I also say Nadam se da ćeš... instead of Nadam se da će ti...?

Not with svidjeti se.

Nadam se da ćeš... would mean I hope you will... followed by an action you perform (a verb where you are the subject), e.g. Nadam se da ćeš doći = I hope you will come.
But with svidjeti se, the “you” is not the subject; it’s the dative experiencer (ti), so you keep će (referring to roman) and use ti: da će ti se svidjeti ovaj roman.