Learn Hardcore Swahili: Familia yetu inacheza mpira jioni. - Our family plays ball in the evening.

Because in Swahili agreement goes with the noun class of the subject. Familia is treated as a third-person singular, class 9 noun, so you use the class 9 subject prefix i-. Tunacheza would come from the first-person plural prefix tu- (“we”), which you’d only use if the subject were the pronoun sisi (“we”).

How is the verb inacheza built up?

inacheza = i- + -na- + cheza

i- = subject prefix for class 9 nouns (here familia)
-na- = present-tense (continuous/habitual) marker
cheza = verb root “play”

Why is the possessive yetu used in familia yetu, and how do I choose the right form?

Possessive pronouns in Swahili agree with the noun class of the thing possessed. Since familia is class 9, its possessive is -etu, giving familia yetu = “our family.” You pick the suffix (-etu, ‑ako, ‑wako, etc.) based on both the owner (our, your, his/her) and the class of the noun possessed.

What does mpira mean here? Is it any kind of ball?

Literally mpira = “ball.” In everyday East African usage kucheza mpira almost always means “play soccer/football.” If you want another ball game you add a qualifier, for example:

mpira wa kikapu = basketball
mpira wa mikono = handball

Why is there no preposition like “in” or “at” before mpira or jioni?

Swahili doesn’t need a preposition between verb and object—objects simply follow the verb (ina-cheza mpira = “(it) plays ball”). Time words work similarly: jioni on its own means “in the evening,” so no extra “in” is required.

What exactly does jioni mean, and how is it different from mchana or usiku?

jioni = “evening” (roughly 6 PM–9 PM)
mchana = “daytime/afternoon”
usiku = “night”
You swap in whichever time-of-day fits your meaning.

Do I always put jioni at the end, or can it appear elsewhere?

Time expressions in Swahili are flexible. The neutral order is Subject–Verb–Object–Time (familia yetu inacheza mpira jioni), but you can front jioni for emphasis:
Jioni, familia yetu inacheza mpira.

What nuance does the -na- in inacheza add? Is it “is playing” vs. “plays”?

The infix -na- is the standard present-tense marker in Swahili. It covers both habitual (“plays regularly”) and continuous (“is playing right now”) senses. There’s no separate English-style distinction; ina-cheza can mean either “(it) plays” or “(it) is playing” depending on context.