Learn Hardcore Japanese: watasi ha yasumi ni haha to issyo ni keeki wo tukurimasu. - I make a cake with my mother on my day off.

は is the topic marker. It tells us that 私 (“I”) is what we’re talking about. It doesn’t necessarily mark the grammatical subject (though here it happens to be both). It sets the stage for the rest of the sentence.

Why is 休み followed by に (i.e. 休みに)?

に marks a point in time when something happens. Here 休みに means “during the break/vacation.” Without に, 休み would just be a noun meaning “holiday/break” with no indication of when the action takes place.

Why do we have both 母と and 一緒に? Isn’t that redundant?

They serve different roles:

母と uses と (“with”) to link you and your mother as participants.
一緒に (“together”) is a noun that needs に to turn it into an adverbial phrase.
Together they mean “together with my mother.” If you dropped 一緒に, 母とケーキを作ります would still mean “I make a cake with my mother,” but it loses the explicit sense of “together.”

Why is ケーキ written in Katakana?

ケーキ is a loanword from English (“cake”). Katakana is normally used for foreign words, onomatopoeia, scientific names, and emphasis.

What form is 作ります, and why is it used instead of 作る?

作ります is the polite non-past form of the verb 作る (“to make”). It can cover both habitual actions (“I make cakes regularly”) and planned future actions (“I will make a cake”). In polite conversation, speakers typically use 〜ます forms rather than the plain dictionary form.

Does 作ります here mean “I will make” or “I make” (habitually)?

Japanese non-past tense is ambiguous between habitual and future. Context decides.

If you’re telling your mom your plan for next week’s holiday, it means “I will make.”
If you’re describing your regular weekend routine, it can mean “I make.”

Can I reorder the phrase so it reads 「私は母と休みにケーキを作ります」?

Yes. Japanese word order is relatively flexible as long as particles indicate each element’s role. Your version is still SOV with correct particles (は, と, に, を), so it’s perfectly natural.

What is the difference between 休み and 休日?

休み is a general word for “break,” “holiday,” or “day off.” It can refer to school breaks, work vacations, weekends, etc.
休日 is more formal, often found in calendars or official schedules, meaning “public holiday” or “non-working day.”

Why do we need を before 作ります in ケーキを作ります?

を marks the direct object of a verb. Here ケーキ is what you’re making, so it takes を to show its role as the thing being acted upon.