Learn Hardcore Swahili: Dada yangu anapenda kusoma peke yake bustanini wakati wa machweo. - My sister likes to read by herself in the garden at sunset.

Anapenda kusoma peke yake… – She likes to read by herself… (her preference, habit)
Anasoma peke yake… – She is reading by herself… (what she is doing right now)

Your sentence is about what she likes to do, so anapenda kusoma is correct.

What does peke yake mean, and can it be used with other people (e.g., “by myself”)?

Peke yake literally means “on its/her/his own” and is used as “by herself / alone”.

You can change the possessive part to match the person:

peke yangu – by myself / alone
peke yako – by yourself
peke yake – by himself / herself
peke yetu – by ourselves
peke yenu – by you (pl.) alone
peke yao – by themselves

So:

Ninapenda kusoma peke yangu. – I like to read by myself.
Wanacheza peke yao. – They are playing by themselves.

Can I use mwenyewe instead of peke yake?

Often, yes, but there is a nuance:

peke yake – emphasizes being alone, without others.
mwenyewe – emphasizes “himself/herself personally”, sometimes “without help” or “in person”.

In many casual contexts, they overlap:

Anapenda kusoma peke yake. – She likes to read alone.
Anapenda kusoma mwenyewe. – She likes to read by herself (without help, by her own effort).

When you specifically mean “alone, with no one else around”, peke yake is the clearest.

Why is it bustanini and not just bustani?

The -ni suffix marks a location, similar to “in/at/on” in English.

bustani – garden
bustanini – in the garden / at the garden

Other examples:

nyumba – house → nyumbani – (at) home
shule – school → shuleni – at school
mezani – at the table (from meza, table)

So bustanini itself already includes the idea of “in/at the garden”; you don’t need an extra word like “in”.

Could I say katika bustani instead of bustanini?

Yes, you can:

katika bustani – in the garden
bustanini – in/at the garden

Both are correct. -ni is shorter and very common in speech.
Katika bustani is slightly more explicit and is common in writing or when you want to emphasize “inside” a place.

Your sentence would still be natural as:

Dada yangu anapenda kusoma peke yake katika bustani wakati wa machweo.

What does wakati wa machweo literally mean?

Literally it is:

wakati – time / period
wa – “of” (genitive linking word)
machweo – sunsets / sunset time (from the verb kuchwa, “to set” used of the sun)

So wakati wa machweo = “the time of sunsets / the time of sunset”, i.e. at (around) sunset.

You could think of it as “during sunset” in natural English.

Why is it wakati wa machweo and not wakati ya machweo or something else?

The linking word (“of”) agrees with the first noun, not the second.

wakati belongs to the U-class (class 11/14-like), whose genitive is wa.
So we get wakati wa… no matter what comes after:

Examples:

wakati wa mchana – time of daytime / during the day
wakati wa mvua – time of rain / during the rainy season
wakati wa machweo – time of sunset / during sunset

That’s why it must be wakati wa, not wakati ya.

Can I move wakati wa machweo to a different place in the sentence?

Yes, time expressions are fairly flexible. All of these are possible and natural:

Dada yangu anapenda kusoma peke yake bustanini wakati wa machweo.
Wakati wa machweo, dada yangu anapenda kusoma peke yake bustanini.
Dada yangu, wakati wa machweo, anapenda kusoma peke yake bustanini.

The default, most neutral position is often at the end, as in your original sentence.