Practicamos geocaching y buscamos el geocaché.

Because Spanish often leaves out subject pronouns when the verb ending already shows who is doing the action.

• practicamos = we practise / we practice
• buscamos = we look for / we search for

So nosotros practicamos and nosotros buscamos are possible, but nosotros is not necessary. Spanish does this much more often than English.

Here, -amos is the first person plural ending, meaning we.

Both verbs are -ar verbs:

• practicar → practicamos
• buscar → buscamos

So the sentence has two verbs with the same subject:

• Practicamos geocaching
• y buscamos el geocaché

That means we do both actions.

Yes. This is a very common learner question.

For many -ar verbs, the nosotros form is the same in:

• the present: we practise / we search
• the preterite: we practised / we searched

So:

• practicamos can mean we practise or we practised
• buscamos can mean we search or we searched

Context tells you which one is meant. If the meaning shown to you is present, then read it as present. But the form itself is ambiguous.

After practicar, Spanish often uses the name of the activity without an article.

For example:

• practicar tenis
• practicar yoga
• practicar senderismo
• practicar geocaching

So Practicamos geocaching sounds natural as We practise/do geocaching.

You might sometimes hear el geocaching in other contexts, but after practicar, leaving out the article is very normal.

Here geocaché refers to a specific object: the cache itself. That is why it takes an article.

• el geocaché = the geocache
• un geocaché = a geocache

So the sentence is talking about looking for a particular cache, not just any cache.

Also, geocaché is treated as masculine, so it uses el.

Because they refer to related but different things, and Spanish often handles borrowed words in different ways.

• geocaching = the activity or hobby
• geocaché = the physical cache

In Spanish, especially in informal or modern usage, the activity is often kept in its English form: geocaching.

The object can appear in a more adapted Spanish-looking form: geocaché.

So the sentence mixes:

• the English borrowing for the activity
• the adapted form for the object

That is not unusual with hobby or tech vocabulary.

The written accent shows that the stress falls on the last syllable:

• ge-o-ca-CHÉ

Without the accent mark, Spanish spelling rules would make you stress it differently.

In Spain, the first g before e is pronounced like a strong throaty h sound, so it starts roughly like:

• heh-oh-ka-CHÉ

The accent mark is there to show the correct stress clearly.

The normal Spanish word for and is y.

It changes to e only before words that begin with an i sound, such as:

• padre e hijo
• España e Italia

But geocaché does not begin with an i sound, so y stays the same:

• Practicamos geocaching y buscamos el geocaché.

Practicar is a good, natural choice for doing a hobby, sport, or activity.

So Practicamos geocaching works well.

You could also hear other possibilities depending on style, such as:

• Hacemos geocaching
• Vamos a hacer geocaching

But practicar gives the idea of engaging in the activity, and it sounds perfectly fine.

Yes, it is understandable and natural.

A speaker from Spain would understand it easily. Depending on context, they might also say:

• Practicamos geocaching y buscamos un geocaché if they mean a geocache
• Hacemos geocaching y buscamos el geocaché in a slightly different style

But the original sentence is perfectly acceptable Spanish.