Kad dođem kući, izut ću čizme, obuti papuče i opet uzeti onaj sivi džemper.

After kad in a time clause, Croatian normally uses the present form, even when the meaning is future. With a perfective verb, dođem means when I arrive / when I get home.

So Kad dođem kući is the normal way to say When I get home.
Kad ću doći? would mean When will I come?, which is a different structure.

Kući is a very common special form meaning home / to home in the sense of direction.

• doći kući = to come home
• ići kući = to go home
• biti kod kuće = to be at home

If you say u kuću, that means into the house, focusing more on entering the building itself.

Croatian future tense uses the auxiliary ću plus the infinitive. When the infinitive comes before ću, standard spelling drops the final -i of the infinitive:

• izuti → izut ću
• obuti → obut ću
• uzeti → uzet ću

So izuti ću is not standard.

Also, ću is a clitic, so it normally cannot stand at the very beginning of the clause. That is why Izut ću čizme is natural here. If another word came first, you could also say something like Ja ću izuti čizme.

Because one future auxiliary can cover several coordinated infinitives when they all have the same subject and time reference.

So:

izut ću čizme, obuti papuče i opet uzeti onaj sivi džemper

works like English:

I will take off my boots, put on slippers, and take that grey sweater again.

Croatian does not need to repeat ću before every verb here.

Because obuti is the verb normally used for footwear.

• obuti cipele / čizme / papuče = put on shoes / boots / slippers
• izuti cipele / čizme / papuče = take off shoes / boots / slippers

By contrast, obući is used for clothes more generally:

• obući kaput
• obući majicu
• obući džemper

So obuti papuče is the natural choice.

They are direct objects, so they are in the accusative case.

In this sentence:

• izuti čizme
• obuti papuče
• uzeti džemper

The forms may look unchanged, but that is normal:

• čizme and papuče are feminine plural inanimate nouns, and their accusative plural looks the same as the nominative plural.
• džemper is masculine singular inanimate, and its accusative singular also looks the same as the nominative singular.

So the case is accusative, even though the form does not visibly change.

Yes, that is a very reasonable question.

Uzeti literally means to take. So if the idea is take that grey sweater again / pick it again / grab it again, then uzeti is fine.

But if the intended meaning is specifically put on that grey sweater again, then many speakers would more naturally say:

... i opet obući onaj sivi džemper.

So uzeti is possible, but it depends on what exactly is meant.

Onaj means that, and sivi means grey.

So:

onaj sivi džemper = that grey sweater

The usual order here is:

demonstrative + adjective + noun

So:

• onaj sivi džemper
• ta crvena haljina
• taj stari kaput

Croatian often uses a demonstrative like onaj, taj, or ovaj where English might simply say the, especially when the object is already known from context.

Opet means again.

Here it modifies uzeti, so opet uzeti means to take again. That placement is very natural.

Croatian word order is fairly flexible, so you may also hear other placements in different contexts, but opet uzeti is a normal and clear choice here.

Because the sentence describes a sequence of single, completed actions:

1. arrive home
2. take off the boots
3. put on the slippers
4. take the grey sweater again

Perfective verbs are very common in this kind of future sequence, because the focus is on the actions being completed.

If you used imperfective verbs instead, the meaning would shift toward repetition, duration, or process rather than a simple one-time sequence.

Yes. Kad dođem kući is a subordinate time clause, and when that clause comes before the main clause, Croatian normally separates it with a comma.

So this punctuation is standard:

Kad dođem kući, izut ću čizme...