Learn Hardcore German: Im Haushalt putze ich zuerst die Küche, danach das Bad. - In the household I first clean the kitchen, then the bathroom.

im is the contraction of in dem (in + the). The preposition in can take dative (location) or accusative (movement). Here it’s a location/context (“in the household”), so it’s dative: masculine der Haushalt → dative dem Haushalt → im Haushalt.

Location: im Bad = in the bathroom (dative)
Movement: ins Bad = into the bathroom (accusative; contraction of in das Bad)

Why is the word order putze ich (verb before subject) instead of ich putze?

German is a verb-second (V2) language. Only one constituent can come before the finite verb. Here, Im Haushalt is placed first for emphasis/context, so the verb (putze) must be second, and the subject (ich) follows: [Im Haushalt] [putze] [ich] … You could also say Ich putze im Haushalt … with the subject first.

Why are die Küche and das Bad in the accusative?

They are the direct objects of the transitive verb putzen (“to clean”). Feminine die Küche stays die in the accusative; neuter das Bad stays das. If it were a masculine noun, you’d see the typical accusative change: der Flur → den Flur.

What’s going on with the comma and the fragment danach das Bad? Isn’t something missing?

The second part is an example of “gapping” (ellipsis): the repeated verb (putze) and subject (ich) are omitted because they’re understood from the first clause. Fully written out it’s: Im Haushalt putze ich zuerst die Küche, danach putze ich das Bad. The comma separates two coordinated main clauses; with the ellipsis, the comma is still correct.

Is danach the same as dann or nachher?

danach = after that (explicitly points back to the previous action); slightly more formal/written.
dann = then/next (very common and neutral in speech).
nachher = afterwards/later (often “a bit later,” sometimes vaguer about the sequence). All can work here; stylistically: … zuerst die Küche, dann/danach das Bad.

What exactly does im Haushalt mean? Could I just say zu Hause?

im Haushalt foregrounds the domain of household chores, like “in the household (context).” zu Hause means “at home” (location). Both are possible, but they highlight slightly different things:

Im Haushalt putze ich … = as part of household duties, I clean …
Zu Hause putze ich … = at home, I clean …

Should I add a possessive, like In meinem Haushalt?

You can, but you don’t have to. In meinem Haushalt emphasizes “in my household (as opposed to others).” The original im Haushalt often reads as generic/the household context presumed from discourse. If you want to stress it’s your place, use the possessive.

Can I repeat the verb instead of leaving it out? Are other versions natural?

Yes. All of these are idiomatic:

Im Haushalt putze ich zuerst die Küche, danach putze ich das Bad.
Ich putze im Haushalt zuerst die Küche und danach das Bad.
Zuerst putze ich die Küche, danach das Bad. The original with gapping is concise and common in writing and speech.

What’s the difference between putzen, aufräumen, reinigen, and sauber machen?

putzen: to clean/scrub (remove dirt) — e.g., die Küche putzen, Fenster putzen.
aufräumen: to tidy up/put things in order — e.g., das Zimmer aufräumen.
reinigen: to clean (more formal/technical/professional) — e.g., Teppich reinigen.
sauber machen: to make clean (colloquial) — e.g., das Bad sauber machen (separable: ich mache das Bad sauber).

Does Bad mean “bath” or “bathroom”? What about Badezimmer, Toilette, WC?

In this context das Bad means “the bathroom” (the room). das Badezimmer is the full word; das Bad is the common short form. For the toilet specifically, use die Toilette or das WC. So:

das Bad putzen = clean the bathroom (sink, shower, toilet, etc.).
die Toilette putzen = clean just the toilet.

Where can I place zuerst? Are other positions possible?

zuerst is a temporal sequencing adverb and is flexible:

Im Haushalt putze ich zuerst die Küche … (as given)
Zuerst putze ich im Haushalt die Küche …
Ich putze zuerst die Küche im Haushalt … (less natural with this particular phrase) It usually sits near the part of the action you’re sequencing. Pair it with danach/dann for clarity.

Is erst the same as zuerst? What about zunächst or als Erstes?

zuerst = first (in a sequence) — safest and unambiguous.
erst can mean “first” in sequences but also “only/not until,” which can be ambiguous: Ich komme erst morgen = not until tomorrow. In your sentence, erst works, but zuerst is clearer.
zunächst = initially/to begin with (slightly formal).
als Erstes = as the first thing (colloquial/formal both fine): Als Erstes putze ich die Küche.

Why are the nouns capitalized, and what are their genders/plurals?

All German nouns are capitalized. Genders/plurals here:

der Haushalt (masc.) → plural die Haushalte
die Küche (fem.) → plural die Küchen
das Bad (neut.) → plural die Bäder (note the umlaut change)

How would this change with a masculine room, like der Flur (hallway)?

Masculine nouns show the accusative -n:

Im Haushalt putze ich zuerst den Flur, danach die Küche. Here, der Flur → den Flur (accusative), while die Küche stays die.