Wir unternehmen heute etwas.

Here unternehmen does not mean run a company. It means to do something, to undertake something, or very often to go do an activity.

So Wir unternehmen heute etwas is a natural way to say that we’re doing something today or we’ve got some kind of plan/activity today.

It often suggests a planned outing, activity, or event rather than just any random action.

Both can relate to doing, but they are not used in exactly the same way.

• machen = the general verb to do / to make
• unternehmen = to undertake, often used for an activity, excursion, plan, or event

So:

• Wir machen heute etwas. = We’re doing something today.
• Wir unternehmen heute etwas. = We’re doing something today, often with the sense of going out, having a plan, or undertaking an activity.

unternehmen can sound a bit more purposeful or activity-focused.

No. unternehmen is inseparable.

That matters because some German verbs with prefixes split apart, but this one does not.

For example:

• Present: Wir unternehmen heute etwas.
• Infinitive: etwas unternehmen
• Past participle: unternommen

Notice there is no extra ge- in the participle:

• correct: Wir haben heute etwas unternommen.
• not: *untergenommen

Because German main clauses usually follow the verb-second rule.

In Wir unternehmen heute etwas:

1. Wir = first element
2. unternehmen = finite verb in second position
3. heute etwas = the rest of the sentence

You could also move another element to the front, but the verb still stays second:

• Heute unternehmen wir etwas.

That is also correct.

That is the most natural order here.

• heute = a time adverb
• etwas = the object, something

German often places time expressions before an indefinite object in a simple sentence like this:

• Wir unternehmen heute etwas.

You may also hear other word orders in special contexts, but they usually add emphasis:

• Wir unternehmen etwas heute.
  This is possible only in a marked context, but it sounds less natural as a neutral sentence.

So for a normal statement, heute before etwas is the best choice.

etwas here is an indefinite pronoun meaning something.

It stands on its own, so there is no article with it.

• etwas = something
• nichts = nothing
• alles = everything

In this sentence, etwas is the thing being undertaken, so it functions as the direct object.

It is in the accusative case, because it is the direct object of unternehmen.

We are undertaking something:

• Wir unternehmen etwas.

With etwas, the form does not change between nominative and accusative, so you cannot see the case from the word itself. You know it is accusative from its role in the sentence.

It is an irregular verb. Its present tense forms are:

• ich unternehme
• du unternimmst
• er/sie/es unternimmt
• wir unternehmen
• ihr unternehmt
• sie/Sie unternehmen

Notice the vowel change in the 2nd and 3rd person singular:

• nehmen → nimmst, nimmt
• unternehmen → unternimmst, unternimmt

In your sentence, wir takes unternehmen:

• Wir unternehmen ...

Yes. It can be used in both everyday and more formal contexts.

Everyday:

• Wir unternehmen heute etwas.
  = We’re doing something today.

More formal or serious:

• Die Firma unternimmt große Anstrengungen.
  = The company is undertaking great efforts.

So the core idea is taking action or undertaking something, but in daily speech it often refers to an activity or outing.

Yes, absolutely.

• Wir unternehmen heute etwas.
• Heute unternehmen wir etwas.

Both are correct.

The difference is emphasis:

• Wir unternehmen heute etwas.
  Neutral statement about what we are doing.
• Heute unternehmen wir etwas.
  Puts more focus on today.

This is a very common feature of German word order: the first position can change, but the finite verb still stays in second position.

Usually with nichts or nicht, depending on what you want to negate.

To negate etwas directly:

• Wir unternehmen heute nichts.
  = We’re not doing anything today.

To negate the whole idea in a more contrastive way, you might use nicht in other structures, but with etwas the most natural opposite is nichts.

A very common past form is the Perfekt:

• Wir haben heute etwas unternommen.
  = We did something today / We have done something today.

Parts:

• haben = auxiliary verb
• unternommen = past participle of unternehmen

This is useful because unternehmen is irregular, and unternommen is a form learners often need to memorize.

It is often a little vague on purpose.

Wir unternehmen heute etwas usually means:

• we have some plan,
• we are not just staying idle,
• we will do some activity,

but it does not say exactly what.

So it can be used when the speaker either does not want to specify the activity yet, or when the exact activity is not important.