Muszę przykleić znaczek na kopertę.

Because Polish often drops subject pronouns when they are not needed.

The form muszę already tells you the subject is I, so Muszę przykleić znaczek na kopertę naturally means I must stick a stamp on the envelope.

You could add ja — Ja muszę przykleić znaczek na kopertę — but that usually adds emphasis, like I have to do it.

Muszę is the 1st person singular form of the verb musieć, which means must / have to.

So:

• muszę = I must / I have to
• dictionary form: musieć

It is a very common verb, and its forms are a bit irregular, so learners usually just memorize them:

• muszę = I must
• musisz = you must
• musi = he/she/it must

This is about aspect, which is very important in Polish.

• przykleić is perfective
• przyklejać is imperfective

Here, przykleić is used because the sentence is about one complete action: getting the stamp attached.

So Muszę przykleić znaczek... means something like:

• I need to stick it on
• I need to get it attached

If you used przyklejać, it would sound more like:

• an ongoing action
• a repeated action
• a general process

For a single stamp on a single envelope, przykleić is the natural choice.

Yes. In this context, znaczek naturally means a postage stamp.

If you want to be extra precise, you can say znaczek pocztowy, but in everyday speech znaczek by itself is usually enough when the context is mailing a letter.

So in this sentence, Polish speakers will understand znaczek as a stamp for mailing.

Because na can take different cases depending on the meaning.

Here the idea is putting something onto a surface, so Polish uses:

• na + accusative for movement/placement onto
• na + locative for location on

So:

• na kopertę = onto the envelope
• na kopercie = on the envelope

Compare:

• Muszę przykleić znaczek na kopertę.
  I need to stick the stamp onto the envelope.

• Znaczek jest na kopercie.
  The stamp is on the envelope.

That is one of the most useful preposition patterns to learn in Polish.

Because koperta is a feminine noun, and after na in this sentence it is in the accusative singular.

For many feminine nouns ending in -a, the accusative singular ends in -ę:

• koperta → kopertę
• książka → książkę
• lampa → lampę

So na kopertę is just the correct accusative form.

Because znaczek is a masculine inanimate noun, and in the accusative singular it usually looks the same as the nominative singular.

So:

• nominative: znaczek
• accusative: znaczek

That is why the form stays the same here.

This is different from many masculine animate nouns, which often do change in the accusative.

No. Polish word order is fairly flexible.

The sentence Muszę przykleić znaczek na kopertę is a normal, neutral order. But other orders are possible if you want to emphasize something:

• Znaczek muszę przykleić na kopertę.
  Emphasis on the stamp

• Na kopertę muszę przykleić znaczek.
  Emphasis on the envelope

Even though word order can move around, the neutral version is the best one for learners to use first.

Often, yes.

Both verbs can work, but nakleić is very common when you mean stick something onto a surface, especially things like:

• a stamp
• a label
• a sticker

So many speakers would very naturally say:

Muszę nakleić znaczek na kopertę.

Meanwhile:

• przykleić = attach/stick
• nakleić = stick onto a surface

Your original sentence is understandable and acceptable, but nakleić znaczek na kopertę may sound a bit more idiomatic in everyday Polish.

Yes, you may hear do koperty, because przykleić coś do czegoś is a normal pattern meaning attach something to something.

But there is a slight difference in feel:

• na kopertę emphasizes the surface the stamp goes onto
• do koperty emphasizes the idea of attaching it to the envelope

With stamps, na kopertę is especially natural because a stamp is placed on the envelope’s surface. So the original version fits the situation very well.