Trade in

Yes. You don't have to turn in the trade immediately. I got my phones today. Got them all set up, then went back to the Apple Store and gave them the trades. They validate everything on the spot, including if there is any damage, then run diagnostics to ensure the phone is internally free of issues and assuming the phone is as you suggested, you'll get the value they offered. If there are any issues, the amount can change depending on the actual condition of the phone.

"Just picked up ..." - where? At an Apple Store? An Authorized Apple Retailer?

Ask them.

You should be able to, at the store today they were having trouble processing trade-ins and they told me I had 14 days to complete it so just come back later.

Ask them.

My Apple Store was also having an issue processing trades, but the manager had a device which accepted our phones. It took a little longer, but they were exceptionally accommodating and the trades went through.

Nice, they couldn’t get mine to work but gave me $10 off the watch band I bought so all good 😁

I said I wasn't leaving without them getting the trades through. They got it done. But good for you getting a $10 discount on a watch band!!