Κατασκηνώνουμε κοντά στο ρυάκι.

Because in Greek, the verb ending already shows the subject.

• κατασκηνώνω = I camp / I am camping
• κατασκηνώνουμε = we camp / we are camping

The ending -ουμε tells you it is 1st person plural (we), so Greek usually does not need a separate word for we unless you want emphasis.

It is the present tense.

In Greek, the present tense can mean either:

• we camp (habitually, in general), or
• we are camping (right now / currently)

So the exact English translation depends on context.

Yes, but usually you do not need it.

• Κατασκηνώνουμε κοντά στο ρυάκι. = normal, neutral
• Εμείς κατασκηνώνουμε κοντά στο ρυάκι. = we camp near the stream, with extra emphasis or contrast

Greek often leaves subject pronouns out because the verb ending already makes the subject clear.

κοντά means near or close.

In this sentence, it works with σε to mean near to / close to something:

• κοντά στο ρυάκι = near the stream

You will often see this pattern:

• κοντά σε...
• κοντά στο / στη / στον... depending on the noun that follows

στο is a contraction of:

• σε = to / at / in / near (depending on context)
• το = the for a neuter singular noun

So:

• σε + το = στο

Here:

• στο ρυάκι = to/at/near the stream
• with κοντά, the whole phrase means near the stream

ρυάκι is a neuter singular noun.

That is why it takes the neuter article το:

• το ρυάκι = the stream / brook

Also, the ending -άκι is very common in Greek and often has a diminutive sense, so ρυάκι can suggest a small stream or brook.

It actually appears in the accusative singular, but for many neuter nouns, the nominative and accusative forms are the same.

So:

• το ρυάκι = nominative
• το ρυάκι = accusative

Because the form is identical, you do not see any change.

No, Greek word order is fairly flexible.

This sentence has a very natural, neutral order:

• Κατασκηνώνουμε κοντά στο ρυάκι.

But other orders are possible for emphasis, for example:

• Κοντά στο ρυάκι κατασκηνώνουμε.

That version might sound more marked, as if emphasizing where we are camping.

A rough pronunciation guide is:

• Κατασκηνώνουμε → ka-ta-skee-NO-oo-me
• κοντά → kon-DA
• στο → sto
• ρυάκι → rya-KI

A few helpful notes:

• The stressed syllable is marked by the written accent: -νώ-, -τά, -ά-
• σκη sounds like ski in English
• ρυ can be tricky for English speakers; it is not exactly like English ree, but rya- is a reasonable approximation to start with

Yes. Greek does not always separate those two meanings the way English does.

So Κατασκηνώνουμε can mean:

• We camp near the stream.
• We are camping near the stream.

Context tells you whether it is a general habit or something happening now.

Yes, depending on the meaning you want.

For example:

• δίπλα στο ρυάκι = next to / beside the stream
• κοντά στο ρυάκι = near the stream

So δίπλα usually sounds closer and more exact than κοντά.
In your sentence, κοντά is a natural choice for near.