Cum pater tandem venit, filiam parvam amplectitur et iterum osculatur.

Because cum can be used in two different ways:

• as a preposition: cum amico = with a friend
• as a conjunction introducing a clause: cum pater venit = when the father comes/came

Here it is followed by a whole clause, pater tandem venit, so it must be the conjunction meaning when.

Pater is nominative singular, because it is the subject of the sentence.

Latin does not have words exactly equivalent to English the or a/an. So pater can mean:

• the father
• a father
• sometimes simply father

The context or translation tells you which is most natural in English.

This is a very common question, because written Latin can be ambiguous here.

Without macrons:

• venit can be comes (present)
• vēnit can be came / has come (perfect)

In many texts, macrons are not written, so you have to decide from context.

In this sentence, since amplectitur and osculatur are present tense, many learners will naturally read venit as comes. But in a narrative, Latin can also mix a past event with vivid present forms, so context matters.

Because this is a straightforward temporal use of cum: when father comes/came.

A simple when clause often uses the indicative.
By contrast, cum often takes the subjunctive when it means something more like:

• since
• although
• when in a more descriptive or circumstantial sense

So here cum ... venit is just a plain time clause.

Because they are deponent verbs.

A deponent verb has:

• passive-looking forms
• but an active meaning

So:

• amplectitur = he embraces
• osculatur = he kisses

Even though the forms look passive to an English-speaking beginner, they are translated actively.

Because it is the direct object of the verbs.

The father is doing the action to the little daughter, so Latin uses the accusative:

• filiam = accusative singular of filia
• parvam = accusative singular feminine of parvus

Even though amplectitur and osculatur are deponent, they still take a direct object just like normal active transitive verbs.

Because the adjective agrees with the noun in:

• gender
• number
• case

Here both words are:

• feminine
• singular
• accusative

So parvam must be describing filiam: the little daughter.

Latin usually does not need an explicit subject pronoun, because the verb ending already tells you the person and number.

• amplectitur = he/she/it embraces
• osculatur = he/she/it kisses

Since pater has already been named, Latin does not need to add is (he). The subject is understood.

Because one object can be understood with both verbs.

So Latin is effectively saying:

• he embraces his little daughter
• and kisses (her) again

Latin often avoids repeating a noun or pronoun when it is already clear. English can do the same: He hugged his daughter and kissed her again. Latin simply leaves the second object understood.

Tandem means at last, finally, or after all this time.

It often suggests that something has been delayed, and there may be a feeling of:

• relief
• impatience
• long waiting

So pater tandem venit is stronger than just pater venit. It gives the sense the father finally comes/arrives.

Iterum means again. Here it goes with osculatur:

• et iterum osculatur = and kisses again

Its position is flexible. Latin word order is freer than English word order, so adverbs like iterum can often move around without changing the basic meaning very much.

Because Latin adjective placement is much freer than English.

Both of these are possible:

• filiam parvam
• parvam filiam

In Latin, the endings show which words belong together, so position is less important than in English. In many contexts, filiam parvam is simply a normal, natural order without any special effect.

Because Latin relies much more on word endings than on word order.

English depends heavily on position:

• the father embraces the daughter
  is different from
• the daughter embraces the father

Latin can be freer because the cases show who is doing what.

So in this sentence:

• pater is the subject
• filiam parvam is the object

no matter where they stand. Latin word order is often used for:

• emphasis
• style
• rhythm
• setting the scene first

Here the cum clause comes first to establish the time: When the father finally comes...