В субботу мы собираемся устроить пикник у озера.

Because with days of the week, Russian usually uses в + accusative to mean on a particular day.

• в субботу = on Saturday
• в понедельник = on Monday
• в пятницу = on Friday

Here, суббота is a feminine noun, and its accusative singular form is субботу.

So:

• В субботу мы собираемся... = On Saturday, we’re planning...

в субботе would not work here for a time expression.

In this sentence, собираемся means we are planning / intending / getting ready to do something.

The verb is собираться, and one of its very common meanings is:

• собираться + infinitive = to be going to / to intend to / to plan to

So:

• мы собираемся устроить пикник = we are planning to have/organize a picnic

Yes, the verb is related to the idea of gathering or getting oneself together, but in everyday Russian, собираться + infinitive is a standard way to talk about plans or intentions.

Examples:

• Я собираюсь поехать в Москву. = I’m going to go to Moscow.
• Мы собираемся посмотреть фильм. = We’re planning to watch a movie.

Because собираться often works like a modal-style verb in Russian: it expresses intention, and the action itself is given by an infinitive.

Structure:

• собираться + infinitive

In your sentence:

• собираемся = are planning / are going to
• устроить = to organize / to have / to arrange

Together:

• мы собираемся устроить пикник = we are planning to have a picnic

This is similar to English:

• We are going to have a picnic
• We plan to have a picnic

This is about verb aspect.

• устроить = perfective
• устраивать = imperfective

Here, устроить пикник refers to a single completed event in the future: one picnic that they intend to arrange/have. Russian normally uses the perfective infinitive after verbs like собираться, хотеть, решить, etc. when the speaker has a specific result in mind.

So:

• собираемся устроить пикник = planning to successfully arrange/have a picnic

Compare:

• Мы собираемся устраивать пикники летом.
  = We’re planning to have picnics during the summer
  (repeated or ongoing activity)

So in your sentence, устроить is used because it refers to one planned picnic as a complete event.

It can be translated in a few natural ways depending on context:

• have a picnic
• organize a picnic
• arrange a picnic

Literally, устроить often has the sense of arrange/set up/make happen.

So устроить пикник suggests a bit more than just attending it: the idea is that the speakers are going to make the picnic happen.

In natural English, though, the best translation is often simply:

• We’re planning to have a picnic by the lake on Saturday.

озера is in the genitive case because it follows the preposition у.

The preposition у usually means:

• by
• near
• at
• sometimes at the home/place of

So:

• у озера = by the lake / near the lake

Important pattern:

• у + genitive

Examples:

• у дома = by the house
• у реки = by the river
• у моря = by the sea

The noun is озеро (lake), and its genitive singular form is озера.

Yes, but the meaning changes slightly.

• у озера = by the lake / near the lake
• около озера = near the lake
• на озере = on the lake / at the lake, depending on context

For a picnic, у озера is very natural because it suggests being beside the lake.

Some nuance:

• у озера often feels like right by the lake
• около озера can sound a bit more neutral, simply near the lake
• на озере might sound more like being at the lake area in general, or even on the lake in some contexts

So у озера is a very good, idiomatic choice for by the lake.

Yes, it could be omitted, because the verb form already shows the subject:

• собираемся = we are planning

So both are possible:

• В субботу мы собираемся устроить пикник у озера.
• В субботу собираемся устроить пикник у озера.

Including мы can:

• make the subject clearer
• add a little emphasis
• sound more explicit or contrastive

Russian often leaves out subject pronouns when they are obvious from the verb ending, but keeping them is also completely normal.

No, Russian word order is fairly flexible.

The sentence you have is a natural neutral order:

• В субботу мы собираемся устроить пикник у озера.

But other orders are also possible, for example:

• Мы собираемся в субботу устроить пикник у озера.
• Пикник у озера мы собираемся устроить в субботу.
• У озера мы собираемся устроить пикник в субботу.

The basic meaning stays the same, but the emphasis changes.

For example:

• putting в субботу first emphasizes the time
• putting пикник у озера first emphasizes the event/location

So Russian word order is often about information focus rather than strict grammatical necessity.

It can suggest both, depending on context.

собираться + infinitive often means:

• to plan to
• to intend to
• to be going to

So this sentence can naturally be understood as:

• On Saturday we’re planning to have a picnic by the lake
• On Saturday we’re going to have a picnic by the lake

The Russian wording usually emphasizes intention rather than a completely fixed scheduled fact.

If you wanted a more definite future statement, Russian might use something like:

• В субботу мы устроим пикник у озера.
  = On Saturday we’ll have a picnic by the lake.

That sounds more straightforward and definite.

A useful breakdown is:

• В субботу — time expression, on Saturday
• мы — we
• собираемся — are planning / are going to
• устроить — infinitive, to arrange / have
• пикник — a picnic
• у озера — location, by the lake

So the structure is roughly:

• Time
  • subject
    • intention verb
      • main action
        • object
          • place

Or more abstractly:

• [When] [who] [plan/intend] [to do what] [where]

This is a very common and useful Russian sentence pattern.