They won’t care if you bring your own device unlocked. If you’re buying from Apple’s website or another 3rd party, it should give the option to select the version between unlocked or carrier specific options like Verizon, AT&T, T-Mobile.

You can buy the locked version from T-Mobile outright if it’s cheaper. If you ever want to change carriers you can get it unlocked after a certain amount of time around 90 days.

Edit: Based on your other comments, you’re buying from Apple directly. The last question relates to if the device is carrier locked. Choose “Connect to any carrier later”.

No idea what the quote is from or if it’s true, a reverse image search led me to this as the oldest reference talking about online censorship.

Yes, paid time off requests or advanced request to use leave (doctor appointment, or other) is typical for any planned absenced in the US.

He’s purring