Возьми не этот стакан, а тот.

This is a very common Russian contrast pattern:

не X, а Y = not X, but Y

So:

Возьми не этот стакан, а тот.
literally: Take not this glass, but that one.

Use а when you are correcting or contrasting one choice with another.

This is about aspect.

• взять → perfective
• брать → imperfective

The imperative возьми comes from взять and usually means take it / pick it up as a single completed action.

The imperative бери comes from брать and can sound more like:

• take it in a general sense,
• go ahead and take it,
• or something habitual/repeated depending on context.

In this sentence, the speaker is telling someone to choose one specific glass, so возьми is very natural.

Because стакан is the direct object, so it is in the accusative case.

For masculine inanimate nouns, the accusative singular looks the same as the nominative singular.

So:

• nominative: стакан
• accusative: стакан

If it were a masculine animate noun, the accusative would often match the genitive instead.

Because in Russian, words like этот and тот can function almost like this one and that one when the noun is obvious from context.

So:

• этот стакан = this glass
• тот = that one

Russian often omits the repeated noun if it is already clear.

You could also say а тот стакан, but а тот is more natural here because стакан has already been mentioned.

They mean:

• этот = this
• тот = that

Usually:

• этот refers to something closer to the speaker, or more immediately relevant
• тот refers to something farther away, or the other one

In real usage, the physical distance is not always the most important thing. Sometimes it is just a contrast between two possible choices: this one vs that one.

This word order is very natural because the contrast is built around the object:

• first the command: Возьми
• then the rejected option: не этот стакан
• then the corrected option: а тот

So the sentence guides the listener through:

1. do the action,
2. not this one,
3. but that one.

Russian word order is flexible, but this version sounds neutral and clear.

Yes, you could. Russian allows different word orders for emphasis.

• Возьми не этот стакан, а тот. → neutral, standard
• Не этот стакан, а тот возьми. → stronger emphasis on the choice between the two glasses

Both are understandable. The original sentence is the most straightforward everyday version.

Not necessarily.

Russian imperatives are very common and are not automatically rude. Whether they sound polite depends on:

• tone of voice,
• relationship between speakers,
• context,
• whether you add polite words.

If you want to make it softer, you can say:

Возьми, пожалуйста, не этот стакан, а тот.
= Please take not this glass, but that one.

So возьми by itself can be perfectly normal, especially in casual speech.

The stress is:

Возьми́ не э́тот стака́н, а тот.

Main stressed syllables:

• возьми́
• э́тот
• стака́н
• тот

In speech, тот may get extra emphasis because it is the corrected choice.

No. Here не does not negate the whole verb.

It does not mean:

• Don’t take this glass

Instead, it negates the object phrase as part of the contrast:

• Take not this glass, but that one

If Russian wanted to say Don’t take this glass, it would usually be:

Не бери этот стакан.

So in your sentence, не belongs to the contrast pattern не ... а ..., not to the verb alone.

Yes, that is possible, but it shifts the structure slightly.

• Возьми не этот стакан, а тот.
  First names the noun, then leaves it out the second time.

• Возьми не этот, а тот стакан.
  First contrasts this and that, then gives the noun at the end.

Both are grammatical. The original version is probably the most natural if the noun is introduced first and then omitted in the second half because it is already understood.