Моя подруга купила жёлтый тюльпан для бабушки.

Because подруга is a feminine singular noun, and the possessive word my has to agree with it.

• мой = masculine singular
• моя = feminine singular
• моё = neuter singular
• мои = plural

So:

• мой друг = my male friend
• моя подруга = my female friend

In this sentence, моя matches подруга.

Подруга is the subject of the sentence, so it is in the nominative case.

The nominative is the basic dictionary form, and it is usually used for the person or thing doing the action.

Here:

• Моя подруга = the person who did the buying

So подруга stays in its nominative singular form.

In the past tense, Russian verbs agree with the subject in gender and number.

The infinitive is купить = to buy.

Past tense forms:

• купил = he bought
• купила = she bought
• купило = it bought
• купили = they bought

Since подруга is feminine, the verb must be купила.

So the ending -а tells you the subject is feminine.

It is in the accusative case, because it is the direct object of the verb купила.

The direct object is the thing that was bought:

• She bought what?
• тюльпан

So тюльпан is accusative singular.

However, because тюльпан is a masculine inanimate noun, its accusative singular looks exactly like its nominative singular.

So:

• nominative: тюльпан
• accusative: тюльпан

They look the same, but their function in the sentence is different.

Because тюльпан is masculine singular inanimate, and in the accusative singular, masculine inanimate nouns keep the same form as the nominative.

The adjective must match the noun, so:

• nominative masculine singular: жёлтый тюльпан
• accusative masculine singular inanimate: жёлтый тюльпан

If the noun were animate, the accusative would usually look like the genitive instead.

For example:

• Я вижу нового студента = I see a new student

But a tulip is inanimate, so:

• купила жёлтый тюльпан

The preposition для means for, and it requires the genitive case.

The dictionary form is:

• бабушка = grandmother

Genitive singular:

• бабушки

So:

• для бабушки = for grandmother / for the grandmother / for her grandmother, depending on context

That is why it is not для бабушка.

Yes, для normally takes the genitive case.

Examples:

• для мамы = for mom
• для друга = for a friend
• для детей = for children

So when you see для, you should expect the noun after it to be in the genitive.

Russian does not have articles like English a, an, and the.

So a sentence like this can mean:

• My friend bought a yellow tulip for grandmother
• My friend bought the yellow tulip for her grandmother

Which one sounds best in English depends on context.

Russian usually leaves this information to:

• context
• word order
• emphasis
• sometimes other words like этот = this, один = one/a certain

Yes. Russian word order is fairly flexible because case endings show the grammatical roles.

The neutral/basic order here is:

• Моя подруга купила жёлтый тюльпан для бабушки.

But you could change it for emphasis:

• Для бабушки моя подруга купила жёлтый тюльпан.
  Emphasizes for grandmother.

• Жёлтый тюльпан моя подруга купила для бабушки.
  Emphasizes yellow tulip.

Even when the order changes, the cases help you understand who did what.

The letter ё is pronounced yo, so жёлтый sounds roughly like ZHYOL-tyy.

Important points:

• ё always indicates stress
• жёлтый is stressed on the first syllable
• in printed Russian, ё is often written as е, so you may also see желтый

But the pronunciation is still жёлтый, not желтый with a plain e sound.

Usually, моя подруга means my female friend, not a romantic girlfriend.

Russian normally uses:

• подруга = female friend
• девушка = girlfriend / young woman, depending on context

So in most cases:

• моя подруга = my friend (female)

A native speaker would usually not understand it as my girlfriend unless the context strongly suggested that.

Because the form бабушки can mean more than one thing, and context tells you which one it is.

It can be:

• genitive singular of бабушка
• nominative plural of бабушка

After для, you need the genitive, so here it must be genitive singular:

• для бабушки = for grandmother

It cannot be nominative plural here, because для does not take the nominative.

A helpful stress pattern is:

• моя́ подру́га купи́ла жёлтый тюльпа́н для ба́бушки

A few notes:

• моя́ = stress on the last syllable
• подру́га = stress on ру
• купи́ла = stress on пи
• жёлтый = stress on жёл
• тюльпа́н = stress on the last syllable
• ба́бушки = stress on the first syllable

Stress is important in Russian because it is not always predictable.