No me gusta despedirme con prisa; prefiero quedarme un minuto más y hablar con calma.

Because gustar works differently from English to like.

In Spanish, gustar is closer to to be pleasing to. So:

• Me gusta = It pleases me / I like it
• No me gusta despedirme con prisa = Saying goodbye in a hurry is not pleasing to me

Here:

• me = to me
• gusta = third person singular, because the thing being liked is the action despedirme con prisa

So the structure is not I like X, but rather X is pleasing to me.

Because both come from reflexive/pronominal verbs:

• despedirse = to say goodbye
• quedarse = to stay / remain

The -me means myself and matches the speaker (yo).

When a reflexive verb is in the infinitive, the pronoun can be attached to the end:

• despedirme = to say goodbye
• quedarme = to stay

You could also see these verbs conjugated like:

• me despido
• me quedo

But after verbs like gustar and preferir, the infinitive is very common:

• No me gusta despedirme...
• Prefiero quedarme...

Because despedir and despedirse are different verbs.

• despedir usually means to dismiss, to fire, or to send off
• despedirse means to say goodbye

So here the reflexive form is required. If you said despedir, it would mean something completely different.

Examples:

• Me despido de mis amigos. = I say goodbye to my friends.
• La empresa despidió a diez trabajadores. = The company fired ten workers.

Because in Spanish, the person you are saying goodbye to can be left out if it is obvious or not important.

The full idea could be:

• No me gusta despedirme de la gente con prisa.

But Spanish often omits information that the listener can easily understand from context. So despedirme by itself is enough here.

Con prisa is a very common expression meaning in a hurry.

Literally, it is with haste/hurry, but in natural English we usually say:

• in a hurry
• rushed
• too quickly

Spanish often uses con + noun in expressions where English uses an adverb or a different preposition.

Examples:

• con calma = calmly / without rushing
• con cuidado = carefully
• con interés = with interest

So despedirme con prisa means to say goodbye in a rushed way.

No — prefiero me quedar is not correct.

After preferir, when you use another verb in the infinitive, Spanish normally does this:

• prefiero + infinitive
• prefiero quedarme
• prefiero hablar
• prefiero esperar

If the infinitive is reflexive, the pronoun is attached to the end:

• quedarme
• marcharme
• levantarme

So prefiero quedarme is the correct structure.

Because hablar is coordinated with quedarme after prefiero.

The structure is:

• prefiero [quedarme un minuto más] y [hablar con calma]

Both verbs depend on prefiero, so both stay in the infinitive:

• prefiero quedarme
• prefiero hablar

Using hablando would change the grammar and would not fit this structure.

Literally, yes: one more minute.

But in everyday Spanish, just like in English, it can also be a soft, approximate way to say:

• a little longer
• just a bit more time

So it may or may not be exactly sixty seconds. It often sounds natural and friendly rather than strictly literal.

Con calma means calmly, without rushing, or at an unhurried pace.

It is a very common expression in Spanish, especially in Spain.

In this sentence it contrasts nicely with con prisa:

• despedirme con prisa = say goodbye in a hurry
• hablar con calma = talk calmly / without rushing

So the sentence sets up a clear contrast between rushing and taking your time.

Because Spanish often omits subject pronouns when the verb ending already shows who the subject is.

• prefiero already tells you the subject is yo
• gusta with me also makes the meaning clear

So:

• Prefiero quedarme... = perfectly natural
• Yo prefiero quedarme... = also possible, but more emphatic

Spanish usually leaves out yo unless the speaker wants contrast, emphasis, or clarity.

The semicolon links two closely related parts of the sentence:

• No me gusta despedirme con prisa
• prefiero quedarme un minuto más y hablar con calma

It is stronger than a comma but softer than a full stop. It shows that the second part contrasts with or explains the first.

You could also write it with a full stop, and it would still be correct:

• No me gusta despedirme con prisa. Prefiero quedarme un minuto más y hablar con calma.

The semicolon simply gives the sentence a slightly more polished written style.