Prima di cuocere le patate, prendo il pelapatate e le sbuccio con calma.

Prima di means before. After prima di, Italian normally uses an infinitive when the subject is the same as in the main clause.

So:

• Prima di cuocere le patate = Before cooking the potatoes / Before I cook the potatoes

Here, the person who cooks is the same person who says prendo and sbuccio, so the infinitive cuocere is the natural choice.

If the subject changes, Italian usually uses prima che + subjunctive instead:

• Prima che tu cuocia le patate, io le lavo.
  Before you cook the potatoes, I wash them.

Italian uses definite articles much more often than English.

So le patate can mean:

• the potatoes
• or sometimes just potatoes, depending on context

In this sentence, it refers to the potatoes being prepared, so le patate is completely natural. English often drops the article in a general sense, but Italian usually keeps it.

Yes. That le means them, and it refers back to le patate.

So:

• le sbuccio = I peel them

Italian often avoids repeating the noun and uses a direct object pronoun instead.

Compare:

• prendo il pelapatate e sbuccio le patate = I take the peeler and peel the potatoes
• prendo il pelapatate e le sbuccio = I take the peeler and peel them

Both are correct. The version with le sounds smoother because le patate was just mentioned.

In Italian, unstressed direct object pronouns usually come before a conjugated verb.

So:

• sbuccio le patate = I peel the potatoes
• le sbuccio = I peel them

This is normal word order in Italian pronouns:

• lo vedo = I see him/it
• la compro = I buy it
• li mangio = I eat them (masculine plural)
• le sbuccio = I peel them (feminine plural)

Because patate is feminine plural, the correct pronoun is le.

Sbuccio is the first person singular present indicative of sbucciare.

So:

• sbucciare = to peel
• io sbuccio = I peel

The sentence uses the present tense:

• prendo = I take
• sbuccio = I peel

This can describe a habitual action, a procedure, or a step-by-step narration.

Sbucciare means to peel, especially to remove the skin/peel from something like potatoes or fruit.

Pelare can also mean to peel, and in many contexts the two are very close.

For potatoes, both can work:

• pelare le patate
• sbucciare le patate

But sbucciare strongly emphasizes removing the outer skin or peel.

Il pelapatate means the potato peeler or simply the peeler.

It is a compound noun:

• from pelare = to peel
• and patate = potatoes

Literally, it is something like potato-peeler.

A final -a often suggests a feminine noun, but it is not a guaranteed rule.

Pelapatate is masculine:

• il pelapatate
• i pelapatate

This happens with some compound nouns and with some other exceptions in Italian. So it is best to learn the noun together with its article.

Italian usually drops subject pronouns when they are not needed, because the verb ending already shows the subject.

• prendo already means I take
• sbuccio already means I peel

You can add io for emphasis or contrast:

• Io prendo il pelapatate, non tu.
  I take the peeler, not you.

But in a neutral sentence, leaving out io is more natural.

Both relate to cooking, but they are not exactly the same.

• cuocere = to cook in the sense of applying heat until food is done
• cucinare = to cook in the broader sense of preparing food

Here, cuocere le patate focuses on the actual cooking of the potatoes. It fits well because the sentence contrasts peeling them first and then cooking them.

Con calma literally means with calm, but in natural English it usually means:

• calmly
• slowly
• without rushing
• taking my time

So le sbuccio con calma suggests that the speaker peels them in an unhurried, careful way.

It is very common and natural because Prima di cuocere le patate is an introductory phrase.

So:

• Prima di cuocere le patate, prendo il pelapatate...

The comma helps readability. In a short sentence, you may sometimes see it omitted, but using it here is standard and clear.

Yes, that is correct.

The difference is mainly stylistic:

• ...e le sbuccio con calma = uses a pronoun, sounds smoother and less repetitive
• ...e sbuccio le patate con calma = repeats the noun, still correct but a little less elegant

Since le patate was just mentioned, Italian often prefers the pronoun le.