Na stolu su dvije pozivnice: jedna za mene, a druga za moju sestru.

Because na can go with different cases depending on the meaning:

• na + accusative = movement onto something
  
  • Stavljam knjigu na stol. = I am putting the book onto the table.
• na + locative = location on something
  
  • Knjiga je na stolu. = The book is on the table.

In your sentence, the invitations are already located on the table, so Croatian uses na stolu.

Stolu is the locative singular form of stol.

The noun stol means table, and after na when it expresses location, Croatian uses the locative case:

• nominative: stol
• locative: stolu

So:

• na stolu = on the table

Su is the 3rd person plural form of biti (to be), and in Croatian it behaves like a clitic, which usually goes in the second position in the sentence.

So the sentence structure is:

• Na stolu = first unit
• su = clitic in second position
• dvije pozivnice = the subject

That is why Croatian says:

• Na stolu su dvije pozivnice

rather than the more English-like order Dvije pozivnice su na stolu.

That said, Dvije pozivnice su na stolu is also possible, but the original version sounds very natural and typical.

Because pozivnica is a feminine noun.

Croatian has different forms of two depending on gender:

• dva for masculine and neuter
• dvije for feminine

Examples:

• dva stola = two tables
• dva pisma = two letters
• dvije pozivnice = two invitations

Since pozivnica is feminine, the correct form is dvije.

After dva/dvije, tri, and četiri, the noun usually appears in a special form that looks like the genitive singular. For pozivnica, that form is pozivnice.

So:

• jedna pozivnica = one invitation
• dvije pozivnice = two invitations
• tri pozivnice = three invitations
• četiri pozivnice = four invitations

This is one of those number patterns that learners simply need to get used to.

Jedna means one, and it matches pozivnica, which is feminine singular.

The sentence first mentions two invitations, and then identifies them one by one:

• jedna za mene = one for me
• a druga za moju sestru = and the other for my sister

Because pozivnica is feminine, both words are feminine too:

• jedna
• druga

If the noun were masculine, you would expect jedan and drugi instead.

Here a links two parallel ideas and can often be translated as and, while, or whereas, depending on context.

In this sentence:

• jedna za mene, a druga za moju sestru

it has the sense of:

• one for me, and the other for my sister

It is not exactly the same as i.
Very roughly:

• i = simple and
• a = and/but/while, often with a mild contrast or comparison

Here, a helps separate the two invitations clearly.

Here druga means the other one, not necessarily second in a strict counting sense.

So:

• jedna ... a druga ... = one ... and the other ...

Croatian often uses this pair very naturally when talking about two items.

Although drugi/druga/drugo can sometimes mean second, in this sentence the best interpretation is the other.

Because the preposition za requires the accusative case.

The pronoun ja is the nominative form, but after za you need the accusative form:

• nominative: ja = I
• accusative: mene = me

So:

• za mene = for me

You cannot say za ja.

Because za takes the accusative, and both the adjective and the noun must match that case.

Base forms:

• moja sestra = my sister

After za, they change to accusative feminine singular:

• moju sestru = my sister

So:

• za moju sestru = for my sister

This shows agreement:

• moja → moju
• sestra → sestru

The colon introduces an explanation or breakdown of what was just mentioned.

First the sentence says:

• Na stolu su dvije pozivnice = There are two invitations on the table

Then after the colon it specifies them:

• jedna za mene, a druga za moju sestru

So the colon works like namely or as follows.

No, not in a normal full sentence like this.

Su is the plural form of to be, and the subject is plural in meaning:

• dvije pozivnice = two invitations

So you need:

• Na stolu su dvije pozivnice

Croatian sometimes omits to be in very informal notes, headlines, or special styles, but in standard full sentences it is required here.

Croatian often uses plain to be where English uses there is/there are.

So English says:

• There are two invitations on the table

Croatian says literally:

• On the table are two invitations

That is a normal and natural way to express existence or presence in Croatian.

No. Croatian does not have articles like English a/an and the.

So pozivnice can mean:

• invitations
• the invitations

depending on context.

Likewise:

• jedna here literally means one, but in English we may naturally say one invitation or one is for me depending on the translation.

Context does the work that articles do in English.

Yes, Croatian word order is fairly flexible, but some orders sound more natural than others depending on focus.

The original:

• Na stolu su dvije pozivnice

is a very natural way to present new information about what is on the table.

You could also say:

• Dvije pozivnice su na stolu

but that shifts the emphasis slightly toward two invitations.

So both are grammatical, but the original is the most natural if you are introducing what is on the table.