Na godišnjem odmoru radije čitam roman na terasi nego gledam e-mail.

It is the locative singular after the preposition na.

Here, na means something like on / during / while on, not physical movement. So:

• na godišnjem odmoru = on vacation / while on annual leave

The base form is godišnji odmor. In the locative singular, both words change:

• godišnji → godišnjem
• odmor → odmoru

A useful contrast:

• na terasi = on the terrace (location, no movement) → locative
• na terasu = onto the terrace (movement toward it) → accusative

Also, in everyday Croatian, people very often shorten this to just na godišnjem.

Radije means rather or preferably, and it is used to compare two actions or choices.

In this sentence:

• radije čitam ... nego gledam ...
• I’d rather read ... than look at ...

It is a very common way to express preference with verbs.

A close alternative is:

• Više volim čitati roman nego gledati e-mail.
• literally: I like reading a novel more than looking at email

So:

• radije + verb = very natural and direct
• više volim + infinitive = also common, slightly more explicit

Croatian often uses the present tense to talk about:

• habits
• general preferences
• what someone typically does

So here the present tense does not only mean right now. It can mean something more like:

• When I’m on vacation, I prefer reading a novel on the terrace rather than looking at email.

That is why čitam and gledam work well here.

If you wanted to make it more specifically future, you could say something like:

• Na godišnjem odmoru radije ću čitati roman na terasi nego gledati e-mail.

Yes, roman is in the accusative singular, because it is the direct object of čitam.

The noun roman is masculine inanimate, and for many masculine inanimate nouns, the accusative singular is the same as the nominative singular.

So:

• nominative: roman
• accusative: roman

The same thing happens with e-mail here:

• gledam e-mail

That is also accusative singular, but it looks the same as the dictionary form.

Because Croatian does not have articles.

English needs words like:

• a
• an
• the

Croatian does not. So roman can mean:

• a novel
• the novel

The exact meaning depends on context.

This is one of the biggest adjustments for English speakers learning Croatian.

Because na terasi is the locative singular after na when it means on / at a place.

The noun is:

• terasa = terrace

After na with location:

• na terasi = on the terrace

If there were movement toward the terrace, Croatian would normally use the accusative:

• idem na terasu = I’m going onto the terrace

So the contrast is:

• na terasi = location
• na terasu = direction / movement

Here nego is the correct word because the sentence compares two actions:

• čitam roman
• gledam e-mail

After radije, Croatian normally uses nego to mean than:

• radije čitam nego gledam

By contrast, od is more often used when comparing nouns or pronouns, especially with comparatives like veći, bolji, stariji, etc.

For example:

• Ivan je stariji od Marka. = Ivan is older than Marko.

So in your sentence, nego is the natural choice because the comparison is between reading and looking at email.

It is grammatical, but whether it sounds perfectly natural depends on what you want to express.

Gledam e-mail can suggest:

• looking at email on a screen
• checking email
• paying attention to email instead of doing something else

In everyday speech, many speakers might also say:

• provjeravam e-mail = I check email
• čitam e-mailove = I read emails
• gledam u e-mail = I’m looking at the email / at my email

So your sentence is understandable and acceptable, but in some contexts another verb might sound more idiomatic.

Yes, Croatian word order is fairly flexible, but this version is the most neutral and natural:

• Na godišnjem odmoru radije čitam roman na terasi nego gledam e-mail.

Putting radije before the first verb is very common because it clearly marks the preference right away.

You can move words around for emphasis, but then the sentence may sound more marked or stylistic. For example:

• Radije na godišnjem odmoru čitam roman na terasi nego gledam e-mail.
• understandable, but less neutral

So the original order is a good standard model for learners.

Yes. Very often people simply say:

• na godišnjem

This is extremely common in everyday Croatian, because godišnji odmor is such a familiar expression.

So both are possible:

• Na godišnjem odmoru radije čitam...
• Na godišnjem radije čitam...

The longer form is a bit fuller and slightly more explicit; the shorter one is very natural in conversation.

Croatian can sometimes leave out a repeated verb if the meaning stays clear, but in this sentence repeating the second verb makes the comparison neat and unambiguous:

• radije čitam roman na terasi nego gledam e-mail

That clearly compares:

• reading a novel with
• looking at email

If you dropped gledam, the sentence would be less clear or could sound incomplete. So repeating both finite verbs is a very natural choice here.