Moja narzeczona lubi białe róże.

Because narzeczona is a feminine noun, and the possessive adjective my has to agree with it in gender.

• mój = my, for a masculine singular noun
• moja = my, for a feminine singular noun
• moje = my, for a neuter singular noun

So:

• mój narzeczony = my fiancé
• moja narzeczona = my fiancée

Polish adjectives and possessives change their endings to match the noun they describe.

Narzeczona means fiancée or bride-to-be: a woman someone is engaged to.

Related forms:

• narzeczony = fiancé
• narzeczona = fiancée

It is more specific than dziewczyna (girlfriend). If you say moja narzeczona, you are saying the woman is your engaged partner, not just your girlfriend.

Because lubić is the infinitive: to like.
In the sentence, you need a conjugated form: likes.

The subject is moja narzeczona = my fiancée, which is third person singular, so the correct form is lubi.

Present tense of lubić:

• ja lubię = I like
• ty lubisz = you like
• on/ona/ono lubi = he/she/it likes
• my lubimy = we like
• wy lubicie = you all like
• oni/one lubią = they like

So Moja narzeczona lubi... = My fiancée likes...

Because the adjective biały (white) has to agree with róże in number, gender, and case.

Here, róże is plural, so the adjective must also be plural.

• singular feminine: biała róża = a white rose
• plural: białe róże = white roses

So:

• biała goes with a singular feminine noun
• białe goes with a plural non-masculine-personal noun like róże

That is why białe róże is correct.

It is in the accusative plural, because it is the direct object of the verb lubić.

The verb lubić normally takes the accusative case:

• Lubię kawę. = I like coffee.
• Lubię psy. = I like dogs.
• Moja narzeczona lubi białe róże. = My fiancée likes white roses.

A useful thing to notice: for many feminine plural nouns, the nominative plural and accusative plural look the same.
So róże can look the same in both cases, even though its role in the sentence is different.

Yes, in normal usage, lubić takes a direct object in the accusative.

Examples:

• Lubię herbatę. = I like tea.
• Lubisz muzykę. = You like music.
• Oni lubią filmy. = They like films.

So in your sentence, białe róże is in the accusative because it is what the fiancée likes.

Yes, Polish word order is more flexible than English, because case endings help show what each word is doing.

The most neutral order here is:

• Moja narzeczona lubi białe róże.

Other orders are possible, but they change the emphasis:

• Białe róże lubi moja narzeczona.
  = It is white roses that my fiancée likes.
• Moja narzeczona białe róże lubi.
  = possible, but marked; it sounds more emphatic or stylistic.

So yes, you can move things around, but the original sentence is the most natural default order for a learner.

No. Polish usually does not require a subject pronoun if the subject is already clear.

Here the subject is explicitly stated:

• Moja narzeczona lubi białe róże.

You would only use ona (she) for emphasis, contrast, or when the subject has not already been named.

For example:

• Ona lubi białe róże, a ja wolę czerwone.
  = She likes white roses, and I prefer red ones.

In your sentence, adding ona would usually be unnecessary.

Because róże is the plural form of róża (rose).

• róża = rose
• róże = roses

So:

• biała róża = a white rose
• białe róże = white roses

The ending -e here helps signal the plural.

A simple approximate pronunciation is:

MO-ya na-zhe-CHO-na LOO-bee BYA-we ROO-zhe

A few useful sound notes:

• j in Polish sounds like English y in yes
  so moja is roughly moya
• cz sounds like ch in chop
• rz and ż usually sound like the zh sound in measure
• ł sounds like English w
• bi in białe starts with a soft bya-type sound

This is only an approximation, but it is a helpful starting point.

Because in the plural, Polish does not simply use the singular feminine ending.

For adjectives in the plural, an important distinction is:

• masculine personal plural: often -i / -y
• non-masculine-personal plural: often -e

Róże is not a masculine-personal noun, so it takes the non-masculine-personal plural adjective form:

• białe róże

Compare:

• biała róża = white rose
• białe róże = white roses
• biali mężczyźni = white men

So even though róża is feminine in the singular, in the plural the adjective form is białe, not białe because feminine singular, but białe because plural non-masculine-personal.

Lubić means to like, while kochać means to love.

So:

• Moja narzeczona lubi białe róże. = My fiancée likes white roses.
• Moja narzeczona kocha białe róże. = My fiancée loves white roses.

English often uses love loosely, but in Polish kochać is stronger.
If you just mean preference or enjoyment, lubić is the normal choice.