If you had your data backed up ahead of time, sure

If you’re THAT anxious about a simple update for your mobile phone, i hope you’re in therapy

Try the SIM in another phone. If that phone doesn’t give the “no SIM” error, then it’s the SIM tray/reader in your phone that has gone bad, and needs to be repaired/replaced

You can’t have both a PIN and a pattern - it can only be one or the other. If you try to factory reset it via the Settings, does it ask you to confirm your screen lock?

No, there’s no way to remove/bypass the screen lock without factory resetting it. The only thing that I can think of to do is to check and see if the IMEI is still clean and if it is, insert an active T-Mobile SIM so that it has a data connection and then see if a message from the owner pops up on the screen. If it has a data connection, they can also remotely locate it, so maybe that would help them find it/you

Few months? No.

Few weeks? Yes.

It shouldn’t need to get a signal. Simply inserting the SIM should be enough to let you proceed thru the setup steps

If they’re sending the code via SMS, you need to transfer your cellular service to a different device