A pesar de que me daban un poco de miedo las cuevas, aquella cueva me pareció tranquila.

A pesar de que means even though, although, or more literally despite the fact that. It introduces a contrast:

• A pesar de que me daban un poco de miedo las cuevas...
• Even though caves scared me a little...

It is very similar to aunque in meaning. The difference is mostly one of style and emphasis:

• aunque = very common, shorter, simpler
• a pesar de que = a bit more explicit and emphatic

So this sentence could also be written as:

• Aunque me daban un poco de miedo las cuevas, aquella cueva me pareció tranquila.

Both are natural.

Spanish often uses the structure dar miedo = to frighten / to scare / to give fear.

So:

• Las cuevas me daban miedo
• literally: Caves gave me fear
• natural English: Caves scared me / I was afraid of caves

The me is an indirect object pronoun meaning to me.

So the structure is:

• [thing] + dar + miedo + a alguien
• Las cuevas me daban miedo
• Dogs give me fear would be Los perros me dan miedo

This is a very common Spanish pattern, even though it does not match English word-for-word.

Daban is the imperfect tense, and it is used here because the sentence is talking about a past ongoing or habitual feeling, not one single completed event.

• me daban miedo las cuevas = caves used to scare me / caves were somewhat scary to me
• me dieron miedo las cuevas would sound more like the caves scared me at a particular moment

In this sentence, the speaker is giving background information: in general, caves were a bit frightening to them. That is why the imperfect fits well.

Un poco de means a little bit of.

So:

• un poco de miedo = a little fear
• more naturally in English: a little scared / a bit afraid

The de is necessary after un poco when it is followed by a noun:

• un poco de agua
• un poco de tiempo
• un poco de miedo

It also softens the statement. The speaker is not saying caves terrified them, only that they were a little afraid.

Because the sentence moves from a general idea to one specific example.

• las cuevas = caves in general
• aquella cueva = that particular cave

So the meaning is:

• Even though caves in general scared me a little, that specific cave seemed calm to me.

This contrast is important. The speaker usually finds caves a bit scary, but this one felt different.

Aquella means that and refers to something relatively distant, whether physically, mentally, or in the story.

Spanish has three common demonstratives:

• esta = this
• esa = that
• aquella = that over there / that one

In practice:

• esta cueva = this cave
• esa cueva = that cave
• aquella cueva = that cave over there / that cave back then / that particular one

Here, aquella gives a sense of distance or recollection. It can sound slightly more vivid or literary than esa.

Me pareció tranquila means it seemed calm to me or I found it calm. It expresses the speaker’s personal impression.

That is different from:

• era tranquila = it was calm
  This sounds more like an objective description or characteristic.
• estaba tranquila = it was calm
  This refers more to its state at that moment.

By saying me pareció tranquila, the speaker is emphasizing perception:

• That cave seemed calm to me
• I felt that cave was calm

It is a very natural choice because the sentence contrasts fear with personal impression.

Because tranquila describes cueva, and cueva is a feminine singular noun.

Agreement in Spanish means adjectives must match the noun in gender and number:

• la cueva tranquila
• el lugar tranquilo
• las cuevas tranquilas

So in:

• aquella cueva me pareció tranquila

both aquella and tranquila are feminine singular to match cueva.

Because a pesar de que is a fixed expression used when it is followed by a full clause.

Compare:

• A pesar de la lluvia... = Despite the rain...
  Here it is followed by a noun phrase, so you use a pesar de.
• A pesar de que llovía... = Even though it was raining...
  Here it is followed by a verb clause, so you use a pesar de que.

In your sentence, me daban un poco de miedo las cuevas is a full clause, so que is needed.

Yes, absolutely. That would also be correct:

• A pesar de que tenía un poco de miedo a las cuevas, aquella cueva me pareció tranquila.

This means almost the same thing. The difference is mainly in expression:

• me daban miedo las cuevas = caves scared me
• tenía miedo a/de las cuevas = I was afraid of caves

Both are common. The version with dar miedo often sounds especially natural when talking about things that frighten someone.

Both are possible.

• Las cuevas me daban un poco de miedo is probably the more neutral order.
• Me daban un poco de miedo las cuevas puts the focus a little later, almost as if the speaker is building up to las cuevas.

Spanish word order is more flexible than English, especially when the meaning is still clear from the verb and pronouns.

In this sentence, the fronted me daban un poco de miedo flows well after a pesar de que and sounds natural.

Not always. Depending on context, me pareció can mean:

• seemed to me
• struck me as
• I found
• I thought

In this sentence:

• aquella cueva me pareció tranquila

possible natural translations include:

• that cave seemed calm to me
• I found that cave calm
• that cave struck me as calm

So the exact English wording can change, even though the Spanish idea stays the same.