O casal beija-se no fim do jantar.

Because casal is a singular noun in Portuguese. It means couple, so it refers to two people as one unit.

That is why the verb is also singular:

• o casal = the couple
• beija = kisses

So O casal beija-se is grammatically the same kind of structure as The couple kisses.

It comes from the verb beijar, meaning to kiss.

• beija = kisses
• se = a clitic pronoun

In this sentence, se gives the idea of a reciprocal action: the two members of the couple kiss each other.

So beija-se here means kiss each other, not just kisses in a general sense.

Here it is best understood as reciprocal.

A reflexive meaning would be something like he kisses himself.
A reciprocal meaning is they kiss each other.

Since o casal refers to two people acting toward one another, the natural interpretation is reciprocal: the couple kiss each other.

This is a very important feature of standard European Portuguese.

In affirmative main clauses, unstressed pronouns like me, te, se, lhe, nos often come after the verb. This is called enclisis.

So:

• beija-se
• levanta-se
• chama-se

The hyphen is required in standard spelling when the pronoun is attached to the verb like this.

In European Portuguese, O casal beija-se is the normal standard form.

O casal se beija sounds much more like Brazilian Portuguese, where putting the pronoun before the verb is much more common.

So if you are learning Portuguese from Portugal, beija-se is the form you should expect and use in this kind of sentence.

They are contractions:

• no = em + o
• do = de + o

So:

• no fim = at/in the end
• do jantar = of the dinner / of the meal

Portuguese uses these contractions very often, so they are something you will see constantly.

Here it is a noun, meaning dinner or the evening meal.

That is clear because it appears in do jantar, where it is part of a noun phrase:

• o jantar = the dinner / the meal
• do jantar = of the dinner / of the meal

Portuguese words like jantar can sometimes be both:

• jantar as a verb = to have dinner
• jantar as a noun = dinner

In this sentence, it is definitely the noun.

Yes, both are possible.

• no fim do jantar = at the end of dinner
• no final do jantar = at the end of dinner

No fim do jantar is very natural and common.
No final do jantar is also correct and natural, just slightly different in style.

So for a learner, the safest idea is that both mean essentially the same thing here.

It is the present indicative of beijar.

In a sentence like this, the present can have different values depending on context, for example:

• a general or habitual action
• a scene being described
• a narrative present

By itself, O casal beija-se no fim do jantar most naturally means something like The couple kiss each other at the end of dinner.

Not naturally in this meaning.

Without se, O casal beija... sounds incomplete, because beijar normally needs an object:

• O casal beija o bebé. = The couple kiss the baby.
• O homem beija a mulher. = The man kisses the woman.

But in your sentence, the idea is that the two people in the couple kiss each other, and se is what expresses that. So beija-se is the right form here.