Дома я сразу надеваю тапки и иду на кухню ставить чайник.

Дома is a very common adverb meaning at home.

• Я дома = I am at home
• Дома я... = At home, I...

В доме usually means in the house/building, focusing more on the physical building rather than the idea of being at home as a normal setting.

So in this sentence, дома is the natural choice.

Yes, often it can.

Russian often drops subject pronouns when the verb form already makes the subject clear:

• Дома сразу надеваю тапки и иду на кухню...

This still clearly means I put on slippers and go to the kitchen...

Including я is not wrong. It can make the sentence a bit clearer, a bit more personal, or just sound natural in context.

Yes, Russian word order is flexible, and сразу can move around.

This version:

• Дома я сразу надеваю тапки...

is neutral and natural.

Other placements are also possible, but they change the emphasis a little:

• Дома сразу я надеваю тапки... — stronger emphasis on I
• Дома я надеваю сразу тапки... — less natural here, but possible in some contexts

Russian word order often reflects emphasis more than strict grammar rules.

Because надевать / надеть is used for putting something on yourself.

• надевать тапки = to put on slippers
• надевать куртку = to put on a jacket

Одевать / одеть usually means to dress someone else:

• одевать ребёнка = to dress a child

A useful rule learners are often taught:

• надеть что-то
• одеть кого-то

So here надеваю тапки is correct.

Тапки is the accusative plural here, because it is the direct object of надеваю.

But for inanimate plural nouns, the accusative is usually the same as the nominative:

• nominative: тапки
• accusative: тапки

So the form does not change.

Also, Russian often uses the plural тапки because people normally mean a pair of slippers.

Because Russian uses the present tense to talk about habits and regular actions, just like English does:

• At home I immediately put on slippers and go to the kitchen...

This is a routine or usual sequence, not just something happening right now.

Also, both verbs are imperfective:

• надевать → надеваю
• идти → иду

Imperfective present is the normal form for repeated, habitual, or ongoing actions.

If you wanted a one-time future meaning, you would more likely say:

• Дома я сразу надену тапки и пойду на кухню...

This is about the difference between the two Russian verbs of motion:

• идти = to go, walking in one direction, as a specific movement
• ходить = to go/walk around, go habitually, or go there and back in a general sense

In this sentence, the speaker describes a concrete sequence of actions:

1. put on slippers
2. go to the kitchen
3. put the kettle on

So иду works well because it presents the movement as a specific step in that sequence.

Хожу would sound more like a general repeated fact, not this immediate next action.

Because на кухню shows movement to the kitchen, while на кухне shows location in/on the kitchen.

• иду на кухню = I go to the kitchen
• я на кухне = I am in the kitchen

This is the usual movement/location contrast:

• на + accusative = motion toward
• на + prepositional = location

So here кухню is accusative because the speaker is moving there.

This is mostly a matter of normal Russian usage.

With кухня, Russian idiomatically uses:

• на кухне = in the kitchen
• на кухню = to the kitchen

Even though English uses in the kitchen, Russian prefers на here. Some place names and locations simply require a particular preposition, and this is one of those cases. It is best to learn на кухне / на кухню as a set phrase.

After verbs of motion, Russian often uses an infinitive to express purpose:

• иду ставить чайник = I am going to put the kettle on
• literally: I go to put the kettle on

So the structure is:

• иду = I go
• ставить чайник = to put the kettle on

This is a very common pattern in Russian:

• иду готовить = I’m going to cook
• пошёл работать = he went to work
• поехали покупать продукты = we went to buy groceries

Literally, ставить means to put / place / set, and чайник means kettle.

But in everyday Russian, ставить чайник commonly means to put the kettle on, meaning to set it up to boil water for tea.

So this is a normal everyday expression, not just a literal idea of physically placing a kettle somewhere.

Also, чайник here is in the accusative singular, but because it is an inanimate masculine noun, the accusative looks the same as the nominative:

• nominative: чайник
• accusative: чайник

Ставить is the imperfective verb, and it sounds very natural here because the sentence describes a normal routine and names the action as part of that routine.

• иду ставить чайник = natural, everyday, routine-like
• иду поставить чайник = also possible, but it can sound a bit more focused on the single completed result

In many purpose constructions after verbs of motion, Russian often uses the imperfective when the speaker is talking about the activity itself in a general or routine way.

So ставить is a very natural choice here.