Я взял талон, чтобы не стоять в очереди.

I took a ticket so as not to stand in line.

Breakdown of Я взял талон, чтобы не стоять в очереди.

• я: I
• в: in
• стоять: to stand
• не: not

Questions & Answers about Я взял талон, чтобы не стоять в очереди.

Why is я included here? Can it be omitted?

Yes, я can often be omitted because the verb ending already shows the subject: взял = (I/he) took (masculine).
People include я for clarity, contrast, or emphasis, especially at the start of a story: Я взял талон... = As for me, I took a ticket...

What does талон mean in this context? Is it the same as билет?

Талон here usually means a numbered ticket/token you take to reserve your place or get called (common in clinics, banks, government offices).
Билет is more like a ticket for transport, events, or entry (train ticket, cinema ticket). In many queue systems, natives say талон (or номерок) rather than билет.

Why is взял used (past tense perfective)? What’s the nuance?

Взял (perfective) focuses on the completed result: you successfully took the ticket.
If you said брал (imperfective), it would sound like a repeated/ongoing/habitual action or background detail, e.g. Я обычно брал талон... = I used to take a ticket...

Why is it взял and not взяла?