Check if iPhone is career free without opening the box

1. You can't. There is northing outside the box that will tell you if it's unlocked or not.
2. You also can't. You need to use the serial number which is printed on the Box, not the IMEI number. The IMEI number is for carrier usage only.

Enter the serial number here for warranty status: Check Your Service and Support Coverage - Apple Support

The warranty status will not display until you activate the device. That's what it is waiting for to display the coverage.

Once you set it up0, it should then update the Check coverage website correctly.