Dopo esserci arrampicati, mangiamo nella radura.

Because dopo here means after doing something that has already been completed. Italian often uses the past infinitive in this pattern:

• dopo + infinitive past
• after having + past participle in English

So:

• Dopo esserci arrampicati = After having climbed / After climbing

Using just arrampicarsi would not express the completed action in the same way.

Here ci is part of the verb arrampicarsi, which means to climb or to climb up, often with the idea of climbing oneself onto something.

So this is not the ci meaning there. It belongs to the verb itself.

Breakdown:

• arrampicare = to climb something
• arrampicarsi = to climb, to climb up, to scramble up

In the past infinitive, the pronoun attaches to the infinitive of the auxiliary:

• essere + ci
• esserci

So esserci arrampicati literally comes from to have climbed ourselves, but in natural English it is simply to have climbed.

Because arrampicarsi is a pronominal/reflexive-type verb, and those normally use essere as the auxiliary in compound tenses.

That is why you get:

• ci siamo arrampicati = we climbed / we climbed up
• dopo esserci arrampicati = after having climbed

Not:

• dopo averci arrampicato ❌

So the auxiliary is essere, not avere.

Because with essere, the past participle agrees with the subject.

The implied subject here is noi = we, so:

• arrampicati = masculine plural or mixed group
• arrampicate = feminine plural

So if the speakers are all female, you would say:

• Dopo esserci arrampicate, mangiamo nella radura.

Because the sentence is describing a sequence from the speaker’s point of view, and Italian often uses the present for a current action or for a habitual/narrative present.

So the logic is:

• first action: after climbing
• next action: we eat

The first action is already completed thanks to dopo esserci arrampicati, while mangiamo gives the main action in the sentence.

This can mean things like:

• After climbing, we eat in the clearing
• Once we’ve climbed up, we eat in the clearing

So there is no tense mistake here.

Here dopo means after.

It can be followed by different things, for example:

• dopo pranzo = after lunch
• dopo la lezione = after the lesson
• dopo aver mangiato = after eating
• dopo esserci arrampicati = after climbing

Another common alternative is a full clause with dopo che:

• Dopo che ci siamo arrampicati, mangiamo nella radura.

That is also correct, though the infinitive structure is often more compact and elegant.

La radura means the clearing, especially an open space in a wood or forest.

Nella is the contraction of:

• in + la = nella

So:

• nella radura = in the clearing

Other similar contractions are:

• nel = in + il
• nei = in + i
• nello = in + lo
• nelle = in + le

Very often, yes, especially when talking about people climbing up somewhere.

For example:

• Mi arrampico sull’albero. = I climb the tree / I climb up the tree.
• Ci siamo arrampicati sulla collina. = We climbed up the hill.

Italian commonly uses the pronominal form arrampicarsi where English just says climb.

So for an English speaker, the reflexive-looking form may feel unusual, but it is very normal in Italian.

Not in natural English. Even though arrampicarsi contains a reflexive element, English does not normally express it that way.

A natural translation is:

• After climbing, we eat in the clearing.
• After we climb up, we eat in the clearing.
• After having climbed, we eat in the clearing.

So you should understand the reflexive part as a feature of Italian grammar, not something you usually reproduce literally in English.