Are settings and accounts (like email) removed when changing the SIM card?
Accounts and data are not removed if you switch the SIM. 

For obvious reasons:
Travelling abroad when you don't want to roam, or getting a new phone/data plan from a different carrier, etc. You could guess how mad people would get if their device got wiped by a SIM switch.

You're not safe, unless you also have set up a screen lock (or full device encryption).

All common smartphones act similar here (Windows Phone/iOS/Android):


If the SIM is locked with a pin, it must be re-unlocked each boot if it's present
If the device has a screen lock, it must be unlocked each boot and if you switch on the screen


I.e, a SIM lock is only bound to your specific SIM and it only prevents misuse of your number and phone/data plan, not the device and its data stored within. As soon as the SIM is replaced or removed, one doesn't need the SIM-PIN to to access the phone. Only a screen lock PIN (or password, unlock gesture or full device encryption) will do.