Lubię wieczorem popatrzeć na gwiazdy z balkonu.

Yes. Lubię means I like, and in Polish it is very common to follow lubić with an infinitive:

• Lubię czytać. = I like to read.
• Lubię spacerować. = I like to walk.
• Lubię wieczorem popatrzeć na gwiazdy z balkonu. = I like to look at the stars from the balcony in the evening.

So structurally, Polish is similar to English here: I like + to do something.

Wieczorem is a very common Polish adverbial form meaning in the evening / during the evening.

It comes from wieczór (evening), but in this sentence it is being used in a fixed time expression. Polish often uses this kind of form for parts of the day:

• rano = in the morning
• wieczorem = in the evening
• nocą = at night / during the night

So wieczorem is the natural choice here.

W wieczór would usually not be used for the general meaning in the evening. It might appear only in more specific or unusual contexts.

This is mainly about aspect.

• patrzeć = imperfective, to look, to be looking
• popatrzeć = perfective, to look for a while / to have a look

In this sentence, popatrzeć suggests a complete, bounded action: to spend a little time looking at the stars.

So:

• Lubię patrzeć na gwiazdy. = I like looking at the stars / more general, ongoing
• Lubię popatrzeć na gwiazdy. = I like to have a look at the stars / spend some time looking at the stars

Both are possible, but popatrzeć gives a nice natural sense of sitting down and enjoying the view for a bit.

Yes, absolutely. That is normal Polish.

After lubić, both imperfective and perfective infinitives can appear, depending on the meaning:

• Lubię czytać. = I like reading
• Lubię przeczytać coś przed snem. = I like to read something through before bed
• Lubię patrzeć na morze. = I like looking at the sea
• Lubię popatrzeć na morze. = I like to gaze at the sea for a while

So popatrzeć works because the speaker likes performing that whole action as a little complete experience.

After patrzeć or popatrzeć, Polish normally uses na + accusative:

• patrzeć na coś = to look at something
• popatrzeć na coś = to have a look at something

So:

• gwiazdy here is accusative plural
• the base noun is gwiazda = star

The full phrase is:

• na gwiazdy = at the stars

Because for many feminine nouns, the accusative plural has the same form as the nominative plural.

Here:

• singular: gwiazda
• nominative plural: gwiazdy
• accusative plural: gwiazdy

So even though the case is accusative after na, the form happens to be the same.

That is very common with non-masculine-personal nouns in Polish.

Both are possible, but they mean slightly different things.

• z balkonu = from the balcony
• na balkonie = on the balcony

In your sentence, z balkonu focuses on the viewpoint: the stars are being watched from that location.

So:

• Lubię wieczorem popatrzeć na gwiazdy z balkonu. = I like to look at the stars from the balcony.

If you said:

• Lubię wieczorem popatrzeć na gwiazdy na balkonie.

that would mean something more like:

• I like to look at the stars while on the balcony.

That is also natural, but the nuance is a little different.

It is genitive singular.

The preposition z can mean from, and in that meaning it takes the genitive:

• z domu = from the house
• z ogrodu = from the garden
• z balkonu = from the balcony

The dictionary form is balkon, and the genitive singular is balkonu.

Yes, the word order is natural.

Lubię wieczorem popatrzeć na gwiazdy z balkonu. sounds good and neutral.

Polish word order is flexible, so you could also say:

• Wieczorem lubię popatrzeć na gwiazdy z balkonu.
• Lubię popatrzeć wieczorem na gwiazdy z balkonu.
• Z balkonu lubię wieczorem popatrzeć na gwiazdy.

These all work, but the emphasis changes a bit:

• Wieczorem first emphasizes when
• Z balkonu first emphasizes from where
• the original version is a balanced, natural statement

In meaning, it most naturally goes with popatrzeć.

So the idea is:

• I like [to look at the stars from the balcony in the evening].

Not:

• In the evening, I like... in a strongly contrastive sense

Of course, in practice the whole sentence is understood smoothly, but semantically wieczorem is mainly telling you when the star-looking happens.

Usually, with the basic meaning look at the stars, the normal expression is:

• patrzeć na gwiazdy
• popatrzeć na gwiazdy

Wpatrywać się w gwiazdy is also possible, but it means something more like:

• to stare into the stars
• to gaze fixedly at the stars

So:

• patrzeć na gwiazdy = neutral, standard
• wpatrywać się w gwiazdy = more poetic or intense

For your sentence, na gwiazdy is the most straightforward and natural choice.

Yes. It sounds natural and idiomatic.

It has a slightly pleasant, reflective tone because of popatrzeć na gwiazdy, but it is still completely normal everyday Polish.

A native speaker would easily understand it as:

• someone enjoys spending some time in the evening looking at the stars from their balcony

The most natural change would be to use the imperfective verb:

• Lubię wieczorem patrzeć na gwiazdy z balkonu.

That sounds more like:

• I like looking at the stars from the balcony in the evening
• a general habit or ongoing activity

With popatrzeć, the sentence suggests more of a complete little action:

• I like to have a look at the stars
• I like to spend a bit of time looking at the stars

So the difference is small, but real:

• patrzeć = more general, ongoing
• popatrzeć = more bounded, for a while, as one little activity