Возьми кружку поменьше, пожалуйста.

Both can mean take, but they are different in aspect.

• возьми is the perfective imperative of взять. It suggests a single, complete action: take one.
• бери is the imperfective imperative of брать. It can sound more like go ahead and take, take it, or take regularly / in general, depending on context.

In Возьми кружку поменьше, пожалуйста, the speaker usually means one concrete action: Please take a smaller mug. That is why возьми is very natural here.

Because it is the direct object of the verb возьми.

The noun кружка is feminine, and feminine nouns ending in -а usually change to -у in the accusative singular:

• nominative: кружка
• accusative: кружку

So:

• Это кружка. = This is a mug.
• Возьми кружку. = Take a mug.

Поменьше means a bit smaller or somewhat smaller.

It comes from меньше (smaller / less) with the prefix по-, which often softens the meaning:

• меньше = smaller
• поменьше = a little smaller, somewhat smaller

So кружку поменьше means a slightly smaller mug or a smaller mug in a softer, more natural way.

Both are possible, but they work differently.

• меньшую is an adjective form agreeing with кружку in case, gender, and number.
• поменьше is an invariable comparative-style form often used colloquially after a noun.

Compare:

• Возьми меньшую кружку. = Take the smaller mug / Take a smaller mug
• Возьми кружку поменьше. = Take a somewhat smaller mug

The version with поменьше often sounds more natural in everyday speech, less stiff, and a bit softer.

Because поменьше here is not behaving like a normal adjective such as маленький or большой.

It is a comparative-style form, and these forms are usually invariable in Russian. They do not agree in gender, number, or case:

• дом побольше = a bigger house
• машину подешевле = a cheaper car
• кружку поменьше = a smaller mug

So even though кружку is accusative feminine singular, поменьше stays поменьше.

They are close, but not identical.

• маленькую кружку = a small mug
• кружку поменьше = a smaller mug, often meaning smaller than this one / smaller than the current option

So поменьше is usually comparative in feeling. It implies comparison with something else, even if that comparison is only understood from context.

For example, if someone offers you a large mug and you want a smaller one, кружку поменьше is very natural.

Yes, it can move around.

In this sentence, пожалуйста at the end is very natural:

• Возьми кружку поменьше, пожалуйста.

But you could also say:

• Пожалуйста, возьми кружку поменьше.
• Возьми, пожалуйста, кружку поменьше.

All are correct. The difference is mostly in rhythm and emphasis, not basic meaning.

By itself, an imperative can sound direct, but it is not automatically rude. A lot depends on:

• relationship between speakers
• tone of voice
• context
• softening words like пожалуйста

So:

• Возьми кружку поменьше. = direct
• Возьми кружку поменьше, пожалуйста. = polite, softened

Still, возьми is singular informal. You would use it with:

• one person you know well
• a child
• a family member
• a friend

If you need formal or plural you, use возьмите.

It would be:

Возьмите кружку поменьше, пожалуйста.

Here:

• возьми = singular informal imperative
• возьмите = plural or formal imperative

So use возьмите when speaking to:

• more than one person
• one person respectfully or formally

Yes, Russian word order is flexible.

The neutral version here is:

• Возьми кружку поменьше, пожалуйста.

But you might also hear:

• Кружку поменьше возьми, пожалуйста.
• Возьми, пожалуйста, кружку поменьше.

The meaning stays basically the same, but the emphasis changes. For example:

• Кружку поменьше... puts early focus on the mug
• ...поменьше naturally highlights smaller

They are similar but not always identical.

• кружка = mug
• чашка = cup

A кружка is usually larger, sturdier, and often used for tea, coffee, or other drinks in a mug. A чашка is usually more like a cup, often smaller and sometimes more delicate.

So if the meaning shown to the learner is mug, then кружка is the right word.

The stress is on the last syllable:

• возьмИ

A rough pronunciation guide:

• возь sounds approximately like voz'
• ми sounds like MEE

A common learner difficulty is the cluster around зьм. The ь is the soft sign, so it softens the preceding consonant.

Also:

• крУжку — stress on кру
• помЕньше — stress on ме
• пожАлуйста — stress on жа

Yes. In Russian, возьми can mean not only physically pick up, but also take / choose / use this one depending on context.

So in a kitchen, shop, or café-like situation, Возьми кружку поменьше, пожалуйста can mean:

• Take a smaller mug
• Choose a smaller mug
• Use a smaller mug instead

Context tells you which shade is intended.