- Is it true that any model number starting with 3 or 5 always means the device is refurbished, rebuilt, or previously repaired?
Refurbished....yes.
Refurbishing is essentially rebuilding or repairing the phone to get it working correctly. That might entail replacing any defective parts and installing a new battery and shrink wrapping the phone and box to make it appear "new".
he also said it is a “swap” device
Sounds like the seller is saying that a user returned the phone because it was defective, and the seller gave the user another phone. But, that's a guess. Ask the seller to explain, since we can only guess at what the seller is really saying.
If this device is really refurbished or swapped, then how did Apple’s official website show it as “Not Activated” before I even opened the box?
It simply means the reworked refurbished device had not been activated. You are the first person to activate the refurbished phone.
The seller told me the iPhone has a 1-year local warranty
You will have to clarify this with the seller. Perhaps they use a local shop that can handle service and repairs, and the seller will cover the costs of any work required..
However, if you take the phone to an authorized Apple service shop, they will not cover anything under warranty. You, or someone else....(the seller?).....will pay for any service that is performed.
If you have to pay for service or repairs, suppose you could try submitting the bill to the seller and ask them to reimburse you as part of the "local" warranty they are talking about.......whatever that might be.
The bottom line here is that you did not buy a "new" phone. You bought a "used / refurbished" phone. Apple cannot help you.