Rândul meu începe acum.

Here, rândul meu means my turn.

The noun rând can mean several things depending on context, such as row, line, order, or turn. In this sentence, it means turn.

So Rândul meu începe acum is literally My turn starts now.

Because Romanian usually uses the definite form of the noun with a possessive adjective in expressions like this.

• rând = a turn
• rândul = the turn
• rândul meu = my turn

Romanian often says possession as the noun + my/your/etc., not just noun + my.

Compare:

• cartea mea = my book
• prietenul meu = my friend
• rândul meu = my turn

So rând meu would sound incomplete or unnatural here.

In Romanian, possessive adjectives usually come after the noun.

So Romanian says:

• cartea mea = my book
• fratele meu = my brother
• rândul meu = my turn

This is normal word order. English puts my before the noun, but Romanian usually places meu / mea / mei / mele after it.

Because rând is a neuter noun, and in the singular, neuter nouns behave like masculine nouns.

That means they take:

• meu in the singular
• not mea

So:

• rândul meu = correct
• rândul mea = incorrect

A useful rule:

• masculine singular: meu
• feminine singular: mea
• neuter singular: also meu

Începe is the 3rd person singular present tense of a începe, meaning to begin / to start.

So:

• a începe = to begin
• începe = begins / starts

The subject is rândul meu, so the verb is in 3rd person singular:

• Rândul meu începe acum = My turn starts now

Because the subject is not I. The subject is rândul meu.

So the sentence is not structured like:

• I start now

It is structured like:

• My turn starts now

Since my turn is a third-person subject, Romanian uses the 3rd person singular verb:

• începe = starts

They are close, but not exactly identical.

• Rândul meu începe acum = My turn starts now
• Acum e rândul meu = It’s my turn now

The second version is often more natural in everyday conversation when you simply want to say it is now your turn.
The given sentence sounds a bit more like your turn is beginning at this moment.

So both are possible, but they are not perfect word-for-word equivalents.

Yes. Romanian word order is fairly flexible.

These are all possible:

• Rândul meu începe acum.
• Acum începe rândul meu.
• Începe acum rândul meu. — possible, but less neutral

The most neutral version of your sentence is the original one. Moving acum can change emphasis:

• Rândul meu începe acum puts a little more focus on the fact that it starts now
• Acum începe rândul meu puts now right at the front for emphasis

A rough pronunciation guide:

• rândul ≈ RUN-dul, but the vowel written â is not a normal English vowel
• începe ≈ in-CHE-pe, but again the first î is that same special Romanian sound

Important point: â and î represent the same sound in modern Romanian.
That sound does not exist in standard English. It is a close central vowel, something like a very tight, central uh.

Also:

• ce in începe is pronounced like che in chess
• stress is usually on -ce-: în-CE-pe

Yes, it is very useful to memorize.

Romanian commonly uses e rândul meu / tău / lui / nostru for turns:

• E rândul meu. = It’s my turn.
• E rândul tău. = It’s your turn.
• Nu e rândul lui. = It’s not his turn.

So even though the noun rând has several meanings, rândul + possessive is a very common pattern for talking about turns.