Can my opponent respond to me playing a unit, for example, I play Sett Brawler to my base, does that start a chain where they can react with say Falling Star? Can you also quote specific rule numbers in the response?

No, your opponent cannot respond to you playing a unit like a "Sett Brawler" (or any unit) directly.

Ruling

When you play a unit, it enters the chain as a pending item, but it does not linger there to allow for a response. According to the rules, units are finalized and removed from the chain immediately, skipping the priority window that would allow an opponent to play a reaction spell like Falling Star.

Why this happens

• Units skip priority: While units do technically enter the chain when played, they do not progress to the "Execute" or "Pass" steps where players gain priority. As stated in the retrieved context: "Units leave the chain directly without a round of priority, unlike spells which linger on the chain."
• No response window: Because the unit leaves the chain immediately upon finalization, there is no finalized chain item for your opponent to target or respond to.

Important Nuance

If the unit you played had a "When you play me" triggered ability, that specific ability would go on the chain after the unit enters the battlefield. In that specific case, your opponent could respond to the ability (not the unit itself) with a reaction spell. However, if the unit has no such triggered abilities, the entire process happens without any opportunity for your opponent to intervene.

Relevant Rules

• Rule 325.1: Players can act during a Chain, but because units skip the priority window, no window is created for them to act.
• FAQ (from retrieved context): "You cannot respond to an opponent playing a unit. Units leave the chain directly without a round of priority, unlike spells which linger on the chain."
• FAQ (from retrieved context): "Players cannot play Reactions in response to permanents (Units, Gear, etc.) being played unless those permanents have triggered abilities."

If you can provide the exact name of the unit you are referring to, I can check if it has any triggered abilities that would create a response window.