Я иду домой по тихой улице.

Because идти and ходить are both verbs of motion, but they are used differently:

• идти = to go in one direction, right now, as a single movement
• ходить = to go habitually, repeatedly, or in different directions

So Я иду домой по тихой улице means I am walking home along a quiet street right now.

If you said Я хожу домой по тихой улице, it would mean something more like I go home along a quiet street as a regular habit.

Yes, it could be omitted.

Russian often leaves out subject pronouns when the verb already makes the subject clear. Since иду already means I am going, Я is not strictly necessary.

So both are possible:

• Я иду домой по тихой улице
• Иду домой по тихой улице

Including Я can add a little emphasis, contrast, or simply make the sentence feel slightly more explicit.

Домой is a very common Russian word meaning homeward / to home / going home.

It is not just the noun дом in a regular case form. It is a special adverb-like word used with motion toward home.

Compare:

• Я иду домой = I am going home
• Я дома = I am at home
• Я иду в дом = I am going into a house/building

So домой is the normal way to say home after a verb of motion.

In modern Russian, домой is usually treated as an adverb, not as a normal noun in a case form.

That is why you do not need a preposition with it here. You simply say:

• идти домой
• ехать домой
• бежать домой

For a learner, the easiest approach is: memorize домой as a fixed word meaning homeward / home after motion verbs.

Here по means something like:

• along
• down
• through a route or area

So по тихой улице means along a quiet street.

This is a very common use of по with movement:

• идти по улице = walk along the street
• гулять по парку = walk around the park
• ехать по дороге = drive along the road

It does not mean on in the English sense here, even though по can have many different meanings in other contexts.

Because the preposition по here requires the dative case.

So:

• улица → улице (dative singular)
• тихая → тихой (dative singular feminine)

That is why you get:

• по тихой улице

Not:

• по тихую улицу

The form тихую улицу would be accusative, which is not used after по in this meaning.

Both words are feminine singular, and both are in the dative case because of по.

Breakdown:

• dictionary form: тихая улица
• dative singular: тихой улице

Changes:

• тихая → тихой
• улица → улице

This is a useful pattern to remember for many feminine nouns and adjectives.

No, Russian word order is fairly flexible.

This version is very natural and neutral:

• Я иду домой по тихой улице

But other orders are possible, depending on emphasis:

• Я по тихой улице иду домой
• Домой я иду по тихой улице
• По тихой улице я иду домой

The basic meaning stays similar, but the focus changes slightly. Russian word order often reflects what is being emphasized rather than strict grammatical rules like in English.

The stress is:

• Я иду́ домо́й по ти́хой у́лице

A rough pronunciation guide:

• я = ya
• иду́ = ee-DOO
• домо́й = da-MOY
• по = pa / po depending on accent and reduction
• ти́хой = TEE-khay
• у́лице = OO-li-tse

A few helpful notes:

• иду́ has stress on the last syllable
• домо́й also has stress on the last syllable
• улице has stress on the first syllable: у́лице

Not if you want the same meaning.

• Я иду домой = I am going home
• Я иду к дому = I am walking toward the house

К дому means movement toward a specific house/building, not necessarily all the way home in the usual everyday sense.

So for going home, домой is the normal choice.

Because тихий often means:

• quiet
• calm
• peaceful
• not noisy

So тихая улица is a quiet street. In context, it usually describes a street with little noise, traffic, or activity.

Then the sentence would simply be:

• Я иду домой по улице

That means I am walking home along the street.

Adding тихой just gives extra description:

• по улице = along the street
• по тихой улице = along the quiet street

So тихой is just an adjective modifying улице.

Иду usually suggests movement on foot, so the most natural translation is I am walking home.

If you wanted to say I am going home in a more general sense, English may allow that, but Russian иду still strongly points to going on foot.

For other kinds of movement, Russian would usually use different verbs:

• еду домой = I am going home by vehicle
• лечу домой = I am flying home
• бегу домой = I am running home