Я взбил яйца венчиком и добавил немного молока.

Взбил is the past tense of взбить, which means to beat/whisk something until it is mixed or foamy. That is the normal verb for eggs in cooking.

• бить by itself usually means to hit or to beat in a more general sense
• взбивать is the imperfective partner of взбить
• взбил is perfective, so it presents the action as completed

So in a sequence like this, Russian naturally uses perfective verbs:

• Я взбил яйца... и добавил молока. = first I finished whisking the eggs, then I added milk.

If you said взбивал, it would sound more like I was whisking or I used to whisk.

It shows that the verb is in the past tense. In Russian past tense, the verb also agrees with the subject in gender and number.

Here:

• взбил = masculine singular
• взбила = feminine singular
• взбило = neuter singular
• взбили = plural

So Я взбил... suggests the speaker is male. If the speaker were female, it would be:

• Я взбила яйца венчиком и добавила немного молока.

The same thing is happening with добавил.

The basic singular form is яйцо = egg.

In this sentence, the speaker is talking about eggs in the plural, so we need the plural form:

• singular: яйцо
• plural: яйца

Here яйца is the accusative plural, because it is the direct object of взбил. But for inanimate nouns in Russian, the accusative plural is usually the same as the nominative plural, so:

• nominative plural: яйца
• accusative plural: яйца

Яиц is a different case: genitive plural. You would use that after quantity words, for example:

• много яиц
• несколько яиц

Because it is in the instrumental case. Russian often uses the instrumental to show the tool or instrument used to do something.

So:

• венчик = whisk
• венчиком = with a whisk / using a whisk

This is very common:

• писать карандашом = to write with a pencil
• резать ножом = to cut with a knife
• есть ложкой = to eat with a spoon

In this sentence, венчиком tells you what the eggs were beaten with.

Because the subject stays the same. In Russian, once the subject is clear, you usually do not repeat it unnecessarily.

So:

• Я взбил яйца венчиком и добавил немного молока.

naturally means:

• I whisked the eggs with a whisk and added a little milk.

The subject of both verbs is still я.

You can repeat я, but it usually adds emphasis or contrast:

• Я взбил яйца, и я добавил молоко.

That sounds more emphatic than neutral.

For the same reason as взбил: добавил is perfective, so it presents the action as a completed whole.

• добавить = to add, complete the act of adding
• добавлять = to be adding, to add repeatedly, or to describe the process

In a simple finished sequence of actions, Russian strongly prefers perfective:

• взбил ... добавил

If you said добавлял, it would suggest more of a process, for example:

• Я медленно добавлял молоко. = I was slowly adding milk.
• Я всегда добавлял немного молока. = I always used to add a little milk.

Because немного requires the following noun to be in the genitive case.

So:

• немного молока = a little milk
• много сахара = a lot of sugar
• мало времени = little time

Here молоко changes to молока, which is the genitive singular form.

This is one of the most important Russian patterns:

• after quantity words like много, мало, немного, the noun usually goes into the genitive

It is genitive singular.

That may feel strange to an English speaker, but it makes sense in Russian because молоко is a mass noun. You are not counting separate individual milks; you are talking about some amount of milk as a substance.

So:

• немного молока = a little milk

Compare that with a count noun:

• немного яиц = a few eggs

There the noun is plural, because eggs are countable.

Yes. Russian word order is much more flexible than English word order. The sentence as given is natural and neutral:

• Я взбил яйца венчиком и добавил немного молока.

But other orders are possible, for example:

• Я венчиком взбил яйца и добавил немного молока.
• Я взбил венчиком яйца и добавил немного молока.

These versions are still grammatical, but the emphasis changes slightly.

Very roughly:

• later position often gives a word a bit more focus
• earlier position often connects it to known information or sets the scene

So the original sentence is a good neutral model, but it is not the only possible order.

Yes, and this is a very common confusion.

• взбил яйца = beat / whisked the eggs
• разбил яйца = broke / cracked the eggs

The prefixes change the meaning a lot:

• вз- in взбить gives the idea of whipping or beating up into a mixture
• раз- in разбить gives the idea of breaking apart

So in cooking:

• разбить яйца = crack the eggs
• взбить яйца = whisk the eggs

Mostly from the meaning of the verbs and from the case forms.

• взбил яйца is a normal verb + direct object combination
• добавил немного молока is also a normal combination, where немного молока functions as what was added

In other words:

• he whisked the eggs
• he added a little milk

Russian case helps mark these relationships, but verb meaning is also very important. Native speakers immediately read the structure as:

1. взбил → яйца
2. добавил → немного молока

The main stress pattern is:

• Я взбил яйца́ ве́нчиком и доба́вил немно́го молока́.

A few useful notes:

• взбил has only one vowel, so the stress is automatically there
• яйца́ is stressed on the last syllable
• ве́нчиком is stressed on the first syllable
• доба́вил is stressed on ба
• немно́го is stressed on но
• молока́ is stressed on the last syllable

Two words that learners often stumble over are:

• взбил because of the consonant cluster взб-
• яйца́ because of the йц combination

They get easier with repetition.

Yes, in the right context it often can be.

Russian does not require subject pronouns as strictly as English does, especially when the subject is already obvious from context. So in a conversation or narrative, you might hear:

• Взбил яйца венчиком и добавил немного молока.

That can still mean I whisked the eggs with a whisk and added a little milk, if the context makes it clear who is speaking.

However, in an isolated example sentence, including я is very normal because it makes the subject explicit.