Quando se despedem, os meus avós beijam-se e desejam-se boa noite.

Not exactly.

• In se despedem, se is part of the verb despedir-se, which means to say goodbye. This is a pronominal verb.
• In beijam-se and desejam-se, se has a reciprocal meaning: each other.

So the sentence contains both:

• a verb that normally comes with se: despedir-se
• verbs where se means one another: beijar-se, desejar-se

This is about clitic placement, and European Portuguese is very particular about it.

• After quando, the pronoun goes before the verb: quando se despedem
• In a normal affirmative main clause, European Portuguese usually puts the pronoun after the verb: beijam-se, desejam-se

So this sentence shows two common patterns:

• subordinate clause: Quando se despedem
• main clause: os meus avós beijam-se e desejam-se boa noite

Because Portuguese often omits the subject when it is already clear.

Here, se despedem means they say goodbye, and the reader understands that they refers to os meus avós in the main clause.

English usually likes to repeat the subject more often. Portuguese, including European Portuguese, does this much less.

You could say Quando os meus avós se despedem..., but it is not necessary here.

Here it means kiss each other.

With a plural subject, se often has a reciprocal meaning:

• Eles beijam-se = They kiss each other

Technically, a reflexive meaning can exist in other contexts, but in this sentence the natural reading is clearly reciprocal, especially because we are talking about two people saying good night.

Because when a clitic pronoun comes after the verb in Portuguese, it is normally attached with a hyphen.

So:

• beijam-se
• desejam-se

But when the pronoun comes before the verb, there is no hyphen:

• se despedem

This is standard Portuguese spelling.

In European Portuguese, it is very common to use the definite article before a possessive:

• o meu pai
• a minha mãe
• os meus avós

So os meus avós is the normal, natural choice in Portugal.

English does not do this, so it can feel redundant to an English speaker, but in Portuguese it is completely standard.

They are all present indicative, third person plural.

• despedem
• beijam
• desejam

Here the present tense describes a habit or usual action, not necessarily something happening right now at this exact moment.

So the idea is: this is what my grandparents normally do when they say goodbye.

In this sentence, it has a strong whenever sense, because the verbs are in the present tense and the sentence describes a repeated habit.

So the idea is:

• Whenever they say goodbye, my grandparents kiss each other and wish each other good night.

In English, when is also possible, but whenever makes the habitual meaning clearer.

The structure is basically:

desejar algo a alguém = to wish something to someone

Here:

• boa noite = the thing being wished
• se = to each other

So desejam-se boa noite means:

• they wish each other good night

In other words, se is the person receiving the wish, and boa noite is what is being wished.

Because noite is a feminine noun.

So the adjective must agree with it:

• boa noite
• not bom noite

This is just normal gender agreement:

• bom dia
• boa tarde
• boa noite

Because boa noite is a fixed expression, just like good night in English.

You do not normally say:

• a boa noite

Here it functions as the standard greeting or wish itself, so Portuguese simply uses boa noite with no article.

This is a very common question.

• avós with ó can mean grandparents or grandmothers, depending on context
• avôs with ô means grandfathers

In os meus avós, the meaning is clearly my grandparents.