Nakon dugog dana ponekad mi najviše treba podrška, a ne savjet.

Because nakon always takes the genitive case in Croatian.

So:

• dan = day
• genitive singular of dan = dana
• dug = long
• to match dana, the adjective also goes into genitive singular masculine: dugog

So nakon dugog dana literally means after a long day.

This is a very common pattern:

• nakon ručka = after lunch
• nakon posla = after work
• nakon dugog putovanja = after a long trip

Ponekad means sometimes.

Yes, it can move around more than an English adverb usually can, because Croatian word order is more flexible. For example:

• Ponekad mi najviše treba podrška.
• Nakon dugog dana mi ponekad najviše treba podrška.

All of these are possible, though some may sound more natural than others depending on what you want to emphasize.

In this sentence, ponekad comes early, which is very natural for a time/frequency adverb.

Mi is the short unstressed form of meni, meaning to me.

It is the dative form of ja.

So:

• meni = to me
• mi = to me (short clitic form)

In this sentence, Croatian uses a structure that is literally closer to:

• To me, support is most needed

So mi treba podrška corresponds to English I need support.

Compare:

• Treba mi pomoć. = I need help.
• Treba mi odmor. = I need rest.

Croatian has more than one way to express need.

A very common pattern is:

• trebati + dative person + nominative thing

So:

• Treba mi podrška.
• literally: Support is needed to me
• natural English: I need support

In this pattern:

• the person who needs something is in the dative: mi
• the thing needed is in the nominative: podrška
• the verb agrees with the thing needed:
  
  • treba for singular
  • trebaju for plural

Examples:

• Treba mi voda. = I need water.
• Trebaju mi nove cipele. = I need new shoes.

You may also hear trebam podršku. That structure exists too and is common in real life. But this sentence uses the dative + treba pattern.

In this sentence, podrška is the grammatical subject of treba, not a direct object.

That is why it stays in the nominative:

• podrška = nominative
• not podršku = accusative

This happens because of the treba mi... construction.

So:

• Treba mi podrška. = I need support.
• Trebam podršku. = I need support.

Both can translate the same way, but the grammar is different.

In the sentence you gave, podrška is nominative because the sentence is built with mi treba...

Because a ne savjet is contrasting with podrška, and it stays in the same grammatical role.

So the structure is:

• podrška, a ne savjet
• support, not advice

Both nouns are functioning as the thing needed.

Also, savjet is a masculine noun whose nominative singular form is savjet. In this sentence, it matches podrška structurally.

A useful extra point: for masculine inanimate nouns, nominative and accusative are often the same anyway, so savjet does not visually show much difference. But here the main reason is that it is parallel to podrška in the same construction.

Here, najviše means most.

It is the superlative form related to više = more.

So:

• više = more
• najviše = most

In this sentence, najviše treba podrška means something like:

• support is what I need most

It does not mean mostly here.
For mostly, Croatian would more often use words like uglavnom or većinom, depending on context.

Yes, Croatian word order is quite flexible, and this sentence is arranged for a natural flow and emphasis.

Current order:

• Nakon dugog dana = after a long day
• ponekad = sometimes
• mi = to me
• najviše treba = is most needed
• podrška = support
• a ne savjet = and not advice

One reason this order works well is that mi is a short unstressed word, and such words usually appear early in the clause.

Also, putting podrška later gives it emphasis, especially because it is immediately contrasted with savjet.

Other versions are possible, such as:

• Ponekad mi nakon dugog dana najviše treba podrška.
• Nakon dugog dana mi ponekad najviše treba podrška.

They all mean roughly the same thing, but the focus shifts slightly.

A ne is a very common way to express contrast between two alternatives.

Here it means:

• support, not advice

It often feels like:

• rather than
• and not
• not X but Y

So this sentence is presenting a contrast:

• what is needed = podrška
• what is not needed = savjet

Ali ne is possible in some contexts, but it usually sounds like a stronger but not. In this sentence, a ne is the more natural, idiomatic choice for a simple contrast between two nouns.

Because Croatian has no articles.

There is no direct equivalent of English a, an, or the.

So:

• podrška can mean support, the support, or some support
• savjet can mean advice, the advice, or a piece of advice

The exact meaning depends on context.

In this sentence, English naturally uses bare nouns too:

• I need support, not advice

So the lack of articles feels especially natural here.