Eu tirei a casca da maçã e cortei o limão às rodelas.

Yes. Eu can be omitted, and Tirei a casca da maçã e cortei o limão às rodelas is perfectly natural.

Portuguese often drops subject pronouns because the verb ending already shows who the subject is:

• tirei = I removed / I took off
• cortei = I cut

Including Eu can:

• add emphasis,
• make the subject extra clear,
• or simply reflect the speaker’s style.

So both versions are correct:

• Eu tirei...
• Tirei...

They are in the pretérito perfeito (simple past).

Here it shows completed actions in the past:

• tirei = I removed / I took off
• cortei = I cut

This tense is used for actions seen as finished. In this sentence, both things happened and were completed:

1. the peel was removed,
2. the lemon was cut.

For an English speaker, this often matches the simple past:

• I removed the peel...
• I cut the lemon...

Both are possible.

• tirar a casca de alguma coisa = to remove the peel/skin from something
• descascar alguma coisa = to peel something

So these are both natural:

• Tirei a casca da maçã
• Descasquei a maçã

The version with tirar a casca is a little more explicit because it literally mentions the peel. A learner should recognize both patterns.

Because da is a contraction of de + a.

The structure is:

• a casca de a maçã → a casca da maçã

This happens very often in Portuguese:

• de + o = do
• de + a = da
• de + os = dos
• de + as = das

Here, a casca da maçã means the peel of the apple.

Portuguese uses definite articles more often than English.

In English, you might sometimes say:

• I peeled an apple and cut lemon into slices or more naturally
• I peeled the apple and cut the lemon into slices

In Portuguese, articles are very common when talking about specific things in the situation:

• a casca
• a maçã
• o limão

So this sentence sounds natural because it refers to a particular apple and a particular lemon.

Às rodelas is a common expression meaning into round slices or simply in slices, especially circular ones.

A rodela is a round slice, like a slice of:

• lemon,
• onion,
• tomato,
• sausage.

So cortar o limão às rodelas means cutting the lemon into round pieces.

Às is the contraction of a + as.

In this expression:

• a + as rodelas → às rodelas

This is part of a common pattern used to describe how something is cut or prepared:

• às rodelas = into round slices
• às fatias = into slices
• aos cubos = into cubes

For a learner, it is best to treat cortar às rodelas as a useful chunk.

Because the lemon is being cut into multiple slices.

A single slice would be:

• uma rodela

But when you cut a lemon this way, you normally get several slices:

• rodelas

So the plural is the natural choice.

Yes. Em rodelas is also natural.

So these are both possible:

• cortei o limão às rodelas
• cortei o limão em rodelas

Both mean essentially the same thing. A learner should understand both forms when hearing or reading Portuguese.

The given word order is very natural:

• Eu tirei a casca da maçã e cortei o limão às rodelas.

You can change things a little, but not all changes sound equally natural.

For example, these are fine:

• Tirei a casca da maçã e cortei o limão às rodelas.
• Eu cortei o limão às rodelas e tirei a casca da maçã.
  This changes the order of the actions.

But às rodelas normally stays close to cortei o limão, because it describes the way the lemon was cut.

Yes, two small but useful points:

• maçã is feminine: a maçã
• limão is masculine: o limão

Also, both are singular here:

• one apple,
• one lemon.

This matters because articles and contractions must agree:

• da maçã = de + a maçã
• o limão = masculine singular article + noun